energies

Article
Strategic Model for Charging a Fleet of Electric Vehicles with
Energy from Renewable Energy Sources
Jacek Caban 1, * , Arkadiusz Małek 2 and Branislav Šarkan 3

1 Department of Automation, Faculty of Mechanical Engineering, Lublin University of Technology,

Nadbystrzycka 36, 20-618 Lublin, Poland
2 Department of Transportation and Informatics, WSEI University in Lublin, Projektowa 4,
20-209 Lublin, Poland; arkadiusz.malek@wsei.lublin.pl
3 Department of Road and Urban Transport, Faculty of Operation and Economics of Transport and
Communications, University of Žilina, Univerzitná 8215/1, 01026 Žilina, Slovakia;
branislav.sarkan@fpedas.uniza.sk
* Correspondence: j.caban@pollub.pl

Abstract: The ever-growing number of electric vehicles requires increasing amounts of energy to
charge their traction batteries. Electric vehicles are the most ecological when the energy for charging
them comes from renewable energy sources. Obtaining electricity from renewable sources such as
photovoltaic systems is also a way to reduce the operating costs of an electric vehicle. However, to
produce cheap electricity from renewable energy sources, you first need to invest in the construction
of a photovoltaic system. The article presents a strategic model for charging a fleet of electric vehicles
with energy from photovoltaic systems. The model is useful for sizing a planned photovoltaic system
to the energy needs of a vehicle fleet. It uses the Metalog family of probability distributions to
determine the probability of producing a given amount of energy needed to power electric vehicle
chargers. Using the model, it is possible to determine the percentage of energy from photovoltaic
systems in the total energy needed to charge a vehicle fleet. The research was carried out on real data
from an operating photovoltaic system with a peak power of 50 kWp. The approach presented in the
strategic model takes into account the geographical and climatic context related to the location of the
photovoltaic system. The model can be used for various renewable energy sources and different sizes
of vehicle fleets with different electricity demands to charge their batteries. The presented model
can be used to manage the energy produced both at the design stage of the photovoltaic system and
Citation: Caban, J.; Małek, A.; Šarkan,
during its operation.
B. Strategic Model for Charging a
Fleet of Electric Vehicles with Energy
from Renewable Energy Sources.
Keywords: electric vehicles; traction batteries; battery charging; renewable energy sources;
Energies 2024, 17, 1264. artificial intelligence
https://doi.org/10.3390/en17051264

Academic Editor: Quanqing Yu

Received: 16 February 2024 1. Introduction

Revised: 28 February 2024 For over ten years, two trends have been visible in Poland, Europe, and around
Accepted: 3 March 2024 the world [1–3]. The first concerns the increasingly widespread use of electric vehicles.
Published: 6 March 2024
Every year, more electric vehicles appear on the streets, powered by electricity from a
traction battery on board the vehicle [4–8]. The second trend is the generation of electricity
from renewable energy sources (RES) [9–13]. Each of these trends was clearly visible
Copyright: © 2024 by the authors.
in 2023 and a strong growth trend is observed in each of them for the following years.
Licensee MDPI, Basel, Switzerland. Electromobility and the production of energy from renewable energy sources have a very
This article is an open access article large impact on the environment and people’s behavior. Each of these trends also causes
distributed under the terms and problems that must be carefully examined to counteract them.
conditions of the Creative Commons Electromobility began to develop dynamically after 2012, when large car companies
Attribution (CC BY) license (https:// such as Nissan, Renault, and Tesla began to introduce new models of electric cars to
creativecommons.org/licenses/by/ the market. Going back a dozen or so years, it must be admitted that they had a very
4.0/). short range and needed a very long time to charge the traction batteries with electricity.

Energies 2024, 17, 1264. https://doi.org/10.3390/en17051264 https://www.mdpi.com/journal/energies

Energies 2024, 17, 1264 2 of 17

The average range of an electric vehicle was approximately 100 km. An even greater
challenge was the lack of public infrastructure for charging them. In Europe, and especially
in Poland, it was almost impossible to find a fast charger with a power of 40 kW. Owners
of electric cars also had a lot of problems due to different standards of plugs found in
vehicles and chargers [14]. However, despite these difficulties, electric vehicles were
gaining recognition among customers due to the advantages that distinguished them over
traditional vehicles with combustion engines [15]. Such advantages include, above all, the
high power of electric traction motors and the very convenient course of the torque as a
function of rotational speed [16]. This meant that electric vehicles were and still are very
dynamic, which is of great importance during urban driving [17]. When driving around
the city in an electric vehicle, you should also notice and appreciate that there is no need
to change gears. The high power and torque available from zero rotational speed to very
high rotational speeds guarantee high vehicle acceleration and flexibility. Electric motors
are also quiet and more trouble-free than combustion engines [18]. The quiet operation
of the vehicle’s engine is of great importance both for the driver, for pedestrians moving
near the vehicles, and also for residents, especially in cities. The scope of operation and
service activities for electric cars is much smaller, which translates into lower costs of
warranty and post-warranty inspections at vehicle service stations. Electric vehicles are
also ecological at the point of use because they do not emit any harmful substances into
the atmosphere [19–21]. The most ecological form of propulsion for all types of vehicles is
electric drive, using electricity generated from RES to charge the battery.
At the beginning of 2024, we have a completely different situation in Poland, Europe,
and the world. There are over 30 million vehicles on the road [22]. Electric vehicle bat-
teries have an energy capacity that allows them to travel over 400 km on a single charge.
The development achieved during the last decade was possible thanks to numerous re-
search and development works carried out at universities and research institutes [23–27]
and automotive concerns. There is a well-developed infrastructure for charging electric
vehicle batteries throughout Europe [28]. It includes 7, 11, and 22 kW AC (alternating
current) supply poles for electric vehicle on-board chargers. They are used to slowly charge
vehicle batteries during longer periods of parking at home, at work, and in public places.
The number of chargers charging vehicle batteries with DC (direct current) with power
ranging from 40 to 250 kW is also constantly growing. Currently, the fastest DC chargers
have a power of 350 kW and are able to charge electric vehicle batteries in 15 min [29].
Such chargers are usually located at gas stations and passenger service areas located on
highways and expressways. Thanks to them, it is possible to travel freely in an elec-
tric vehicle throughout Europe. Scientists in research institutes and engineers in large
automotive companies are improving technologies for wirelessly charging batteries in
vehicles [30]. Owners of electric vehicles can use applications on mobile devices and those
built into the vehicle to plan an electric vehicle route, including battery charging points.
Thanks to high competition in the automotive industry, especially from American and
Chinese manufacturers, the prices of electric cars are decreasing, and they are becoming
available to an increasing number of people. The development of electromobility is also
supported by various types of government incentives and other forms of subsidies for
owners of electric vehicles. In this area, it is worth presenting the proposals available in
Slovakia [31,32] or Romania [33] and Scandinavian countries [34,35].
Tens of millions of electric vehicles require very large amounts of electricity to power
them. And this is where new technologies in the field of RES come to the rescue. In Europe
and around the world, the most popular among them are photovoltaic systems (PV) capable
of producing electricity from solar radiation and wind turbine systems that convert kinetic
energy of winds into electricity. Driving on the highway through European countries, you
can easily see large ground-mounted photovoltaic systems with an area of several hectares,
generating peak powers of several MWp. They consist of thousands of individual panels
made using monocrystalline technology. The newest of them produce electricity using
both sides of the panel and are called bifacial panels. The landscape of large photovoltaic
Energies 2024, 17, 1264 3 of 17

systems is often complemented by wind turbines over 200 m high, which already have
a capacity of over 3 MW each. Both of these RES are characterized by periodicity and
variability in the amount of energy produced. Photovoltaic systems produce electricity
only during the day when the sun is shining. Wind turbines produce energy only when the
wind blows.
Therefore, the best solution is to charge electric vehicles with energy from a mix of
energy generated using PV systems and wind turbines. Then, only a small amount of
energy would come from the power grid and would come from burning fossil fuels such as
coal. This would occur when the sun is not shining and the wind is not blowing. However,
investments in renewable energy technologies pose many challenges [36]. One of them is
the capacity of the power grid [37]. At times of high sunlight, high wind, and low demand
for power received from the power grid, the voltage in the network may increase above
the permissible voltage in order to protect electrical receivers. This involves turning off
the inverters and deactivating the fans. People who invested in renewable energy will not
only not earn any money but will also have to pay extra for supplying energy to the grid at
such times [38]. Such moments may therefore be an opportunity to charge the batteries of
electric vehicles with very cheap electricity, which will reduce the costs of individual and
collective transport [39,40].
The aim of the article is to create a strategic model for charging electric vehicles with
energy from RES in the form of ground-based PV systems. Archived data on the daily
amount of energy produced by a ground-based PV system with a peak power of 40 kWp
will be used for this purpose. These will then be processed using the Metalog family of
probability distributions to model daily electricity production. Then, knowledge about the
expected amount of electricity produced will be obtained from the knowledge base in the
form of a mathematical model, accurate to the probability distribution.
Metalog is a flexible probability distribution that can be used to model a wide range
of density functions using only a small number of parameters obtained from experts.
Scientists prefer using the Metalog family of distributions to describe processes in various
fields of science such as theology [41], mathematics [42], and electronics [43]. The authors
have already used Metalog probability distribution families to select the peak power of a
photovoltaic carport for an electric vehicle [44].
The research presented in the article may be helpful to renewable energy developers
who plan to build new generating capacity to power large fleets of electric vehicles [45].
They can also be helpful to private individuals or local governments that have problems
with balancing the energy network in larger or smaller areas [46]. Large numbers of electric
vehicles with traction batteries with high energy capacity may be helpful for this purpose.
Electric buses with batteries with a capacity of over 200 kWh and passenger vehicles
with batteries with a capacity of up to 100 kWh can be charged with DC chargers with
adjustable output power [47]. This solution is also helpful for owners of PV systems who
have built a system with too much power and are unable to use the energy produced.
The solution to this problem is to purchase an electric vehicle with a battery with an
appropriate energy capacity.

2. Research Methodology
The authors proposed to use the Metalog family of probability distributions to de-
termine electricity production. Using this method, it is possible to determine the amount
of energy produced on a daily, monthly, or yearly basis with accuracy to the probability
distribution [48]. The amount of electricity produced on individual days of the month by a
roof-based photovoltaic system with a peak power of 50 kWp will be used to determine the
cumulative distribution function (CDF). This is a continuous function. Then, the probability
distribution function will be determined. The authors used GeNIe 4.1 Academic software
for calculations. It has built-in families of Metalog distributions and allows for quick
determination of the empirical distributor, probability density function, and a simple way
of obtaining information from the knowledge base [49]. The Metalog approach used in
Energies 2024, 17, 1264 4 of 17

the software provides a lot of information about the composition of probability distribu-
tions [50]. Using the Metalog family of distributions, it is possible to obtain information
from a knowledge base and not from a database. In a database, answers to questions are
obtained by searching the database, while a knowledge base answers questions by running
an inference algorithm, which is a fundamental difference.

3. Characteristics of Energy Production from Photovoltaic Systems in Poland

(City of Lublin)
When making conceptual assumptions regarding the size of the photovoltaic system
for charging vehicle batteries, the owner of the vehicle fleet should take into account the
geographical and climatic context related to the location of the photovoltaic system. It is
common knowledge that the expected amount of energy produced depends primarily on
the location of the system and its location on the ground or on the roof of the building. There
are also special photovoltaic structures called carports, which also protect the vehicle against
excessive heating by the sun [40]. The peak power and the type of photovoltaic panels
used have a significant impact on the amount of energy produced. In 2024, monocrystalline
panels are used almost exclusively, and wherever justified, the bifacial version is used.
Panels installed on the ground and in carports can then also generate electricity through
the lower part of the panels [51]. In this way, the amount of energy produced from the
same unit of surface increases. The azimuth and angle of inclination of the panels are also
important. The place intended for a photovoltaic system should not be permanently or
temporarily shaded by buildings or trees. Climatic factors also influence the amount of
energy produced. Local cloud cover and windy conditions significantly affect the amount
of energy produced by photovoltaic systems that are close to each other.
The European Commission collects, monitors, and makes available databases enabling
the determination of the amount of electricity produced monthly by photovoltaic systems
located in various places in Europe. It was decided to check the operation of such an online
platform. The results obtained from it may be important in the preliminary determination
of monthly amounts of energy produced for charging a fleet of electric vehicles.
A photovoltaic system located in the Lublin Voivodeship was selected for research
under Polish geographical and climatic conditions. It is worth emphasizing that it has the
best sunshine in Poland. The intensity of solar radiation is, of course, different in individual
regions of Poland and ranges from 900 kWh/m2 to 1200 kWh/m2 . In order to determine
the properties of a photovoltaic system mounted on a roof and located in Poland, in the
specific city of Lublin, the above-mentioned Internet platform was used. It is based on a
database of installations from various European countries. It allows you to generate the
properties of a photovoltaic system connected to the power grid and export data in the
form of charts or in csv format. The platform allows you to generate the performance of a
photovoltaic system with a specific peak power, taking the following into account:
• Geographic location;
• System installation locations (ground, roof);
• Photovoltaic panel technology;
• Start the system;
• The angle of inclination of the panels;
• Azimuth.
The appearance of the Internet platform window for determining the properties of a
photovoltaic system is shown in Figure 1.
The results obtained from the Internet platform allow for a preliminary estimate of
the amount of energy produced by a photovoltaic system with specific power and design
parameters located in a specific geographical context. However, based on the results
presented in Figure 2, it can be clearly stated that the amount of energy produced per
month varies significantly depending on the month of production, i.e., on the seasonality
of the seasons.
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FOR PEER
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Figure
Figure 1.
1. Properties
Properties of
of aaa photovoltaic
photovoltaic system
system with
with aaa peak
peak power
power of
of 50
50 kWp
kWp connected
connected to the
the power
Figure 1. Properties of photovoltaic system with peak power of 50 kWp connected to
to the power
power
grid
grid located
located in
in Poland
Poland in
in the
the city
city of
of Lublin.
Lublin.
grid located in Poland in the city of Lublin.

The
The amounts
The amounts of
amounts of monthly
of monthly energy
monthly energy production
energy production by
production by aaa photovoltaic
by photovoltaic system
photovoltaic system with
system with aaa peak
with peak
peak
power
power of
of 50
50 kWp
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located in
in Poland
Poland in
in the
the city
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are shown
shown in
in Figure
Figure
power of 50 kWp located in Poland in the city of Lublin are shown in Figure 2. 2.
2.

2. Amounts of
Figure 2.
Figure of monthly energy
energy production byby a photovoltaic system
system with aa peak
peak power of
of
Figure 2. Amounts
Amounts of monthly
monthly energy production
production by aa photovoltaic
photovoltaic system with
with a peak power
power of
50
50 kWp
50 kWp located
kWp located in
located in Poland
in Poland in
Poland in the
in the city
the city of
city of Lublin.
of Lublin.
Lublin.
4. Case Study of Electricity Production for Charging a Vehicle Fleet
The
The results
results obtained
obtained fromfrom thethe Internet
Internet platform
platform allow
allow for
for aa preliminary
preliminary estimate
estimate of
of
4.1. Characteristics of the Photovoltaic System
the
the amount
amount ofof energy
energy produced
produced by by aa photovoltaic
photovoltaic system
system with
with specific
specific power
power and
and design
design
The authors ofin
parameters this article have many years of experience in monitoring the perfor-
parameters located
located in aa specific
specific geographical
geographical context.
context. However,
However, basedbased on
on the
the results
results pre-
pre-
mance in
sented and management of photovoltaic systems. This experience gives rise to anper
approach
sented in Figure
Figure 2,2, it
it can
can be
be clearly
clearly stated
stated that
that the
the amount
amount of of energy
energy produced
produced per month
month
to modeling
varies the amount of energy produced. Trends currently visible in the market include
varies significantly
significantly depending
depending on on the
the month
month of of production,
production, i.e.,
i.e., on
on the
the seasonality
seasonality of
of the
the
the installation
seasons. of panels on flat roofs of institutional and corporate buildings. Photovoltaic
seasons.
panels are then mounted on structures not permanently attached to the roof at much
smaller angles of inclination. Also, the direction of installation of the panels is not oriented
towards the south. An increasing number of individual and institutional investors have
decided to orient their panels to the east and west. Eastern orientation allows you to
 proach to modeling the amount of energy produced. Trends currently visible in the mar-
ket include the installation of panels on flat roofs of institutional and corporate buildings.
Photovoltaic panels are then mounted on structures not permanently attached to the roof
at much smaller angles of inclination. Also, the direction of installation of the panels is not
Energies 2024, 17, 1264 6 of 17
oriented towards the south. An increasing number of individual and institutional inves-
tors have decided to orient their panels to the east and west. Eastern orientation allows
you to maximize the amount of energy produced in the morning. The western orientation
maximize
allows you thetoamount
maximize of energy
the amountproduced in the produced
of energy morning. The western
in the orientation
afternoon. allows
Both the east
you to maximize the amount of energy produced in the afternoon. Both the east
and west orientation of the panels are characterized by less energy produced at high noon. and west
orientation
Due to the of the amount
large panels are characterized
of energy producedby less energy produced
by photovoltaic at high
systems noon.
at high Dueand
noon to
the large amount of energy produced by photovoltaic systems at high noon and
their lack of reception, excessive voltage increases in the power grid very often occur. Grid their lack
of reception,
balancing excessivelead
problems voltage increases in
to individual the power grid
photovoltaic very often
inverters beingoccur.
turned Grid
off balancing
to protect
problems lead to individual photovoltaic inverters being turned off to protect the loads.
the loads. This means the idle operation of the entire system or several photovoltaic sys-
This means the idle operation of the entire system or several photovoltaic systems in the
tems in the area until the voltage in the network drops.
area until the voltage in the network drops.
The research used a photovoltaic system located on the roof of the Lublin WSEI Acad-
The research used a photovoltaic system located on the roof of the Lublin WSEI
emy (Figure 3). The panels were mounted at an angle of 15°, azimuth 295°. The appearance
Academy (Figure 3). The panels were mounted at an angle of 15◦ , azimuth 295◦ .
of the photovoltaic system is shown in Figure 3. The photovoltaic system produced over
The appearance of the photovoltaic system is shown in Figure 3. The photovoltaic system
45 MWh of energy in 2023. The most efficient month in terms of energy production from
produced over 45 MWh of energy in 2023. The most efficient month in terms of energy
this photovoltaic system was May when the system produced 7.7 MWh. The amount of
production from this photovoltaic system was May when the system produced 7.7 MWh.
energy produced on individual days of May 2023 is shown in Figure 4. The system pro-
The amount of energy produced on individual days of May 2023 is shown in Figure 4.
duced a similar amount of energy (7.5 MWh) in July. Due to Polish geographical and cli-
The system produced a similar amount of energy (7.5 MWh) in July. Due to Polish ge-
matic conditions,
ographical there are
and climatic favorablethere
conditions, conditions for theconditions
are favorable productionforof the
electricity only of
production in
selected months of the year. Monthly amounts of energy produced from
electricity only in selected months of the year. Monthly amounts of energy produced from a photovoltaic
asystem with a system
photovoltaic peak power
with of 50 kWp
a peak higher
power than
of 50 kWp2 MWh
highercan be2counted
than MWh can onbein counted
the monthson
from March to October. In the autumn and winter months from November
in the months from March to October. In the autumn and winter months from November to February,
energy
to production
February, energy in Polish geographical
production and climaticand
in Polish geographical conditions
climaticisconditions
very low.is very low.

Figure3.3. Appearance
Figure Appearanceofofaaphotovoltaic
photovoltaicsystem
systemwith
witha apeak
peakpower
powerofof5050kWp
kWpplaced
placedonon the
the roof
roof of of
a
a university building.
university building.

Much more information than the monthly energy production by the photovoltaic
system is provided by the amount of energy produced on individual days of the month.
The month with the highest energy production can be used to determine the maximum
daily amount of energy produced. As we can see in Figure 4, a 50 kWh system is able to
produce over 300,000 Wh or 300 kWh per day.
The authors specifically selected a PV system with a peak power of 50 kWp for
the study. This is the maximum power value for micro-installations that can be built in
Poland by individual users and companies. Contrary to appearances, the energy produced
in one day from such an installation can power quite a large fleet of vehicles. Let us
use examples of electric vehicles from the Renault family. One of the authors is the
owner of an electric vehicle Renault Twizy, which has a traction battery with a capacity of
6 kWh. The Renault Kangoo small delivery vehicle has a traction battery with a capacity of
Energies 2024, 17, 1264 7 of 17

45 kWh. The Renault Zoe, one of the best-selling vehicles in Europe at the time, had batteries
with a capacity of 22 kWh at the beginning of production and then 41 kWh. The Renault
Energies 2024, 17, x FOR PEER REVIEWMegane E Tech car is a five-seater electric SUV. It has a battery with a capacity of 40 7 ofand
18
60 kWh to choose from. However, the large Renault Master delivery vehicle has a traction
battery with a capacity of 40 or 87 kWh. Therefore, the energy produced during one day
of work
Much can be used
more to chargethan
information several to a dozen
the monthly or so vehicles
energy from
production byzero
the to full. There
photovoltaic
are, of course, vehicles with large battery capacities. An example would be a Tesla model
system is provided by the amount of energy produced on individual days of the month.
S with a battery capacity of over 100 kWh or an Audi e-tron GT with a capacity of over
The month with the highest energy production can be used to determine the maximum
90 kWh. Electric buses often have sets of traction batteries with a total energy capacity of
daily amount of energy produced. As we can see in Figure 4, a 50 kWh system is able to
over 200 kWh. For the latter vehicle fleets, PV systems with much higher peak powers
produce over 300,000 Wh or 300 kWh per day.
should be considered than those presented by the authors in this article.

Figure
Figure4.4.Appearance
Appearanceof
ofamounts
amountsof
ofdaily
dailyenergy
energyproduction
productionby
byaaphotovoltaic
photovoltaicsystem
systemwith
withaapeak
peak
power
powerofof5050kWp
kWpininMay
May2023.
2023.

4.2. Charging
The authors a Fleet of Vehiclesselected
specifically from Renewable Energywith
a PV system Sourcesa peak power of 50 kWp for the
study.Many
This is the maximum
people questionpower
the real value for micro-installations
ecology of electric vehiclesthat [20].can be built
When theirinbatteries
Poland
areindividual
by charged withuserselectricity generated
and companies. in coal-fired
Contrary power plants,
to appearances, the energytheyproduced
are not actually
in one
emission-free vehicles. They are emission-free vehicles only at the
day from such an installation can power quite a large fleet of vehicles. Let us use examples point of use because
they
of do not
electric produce
vehicles fromanytheharmful
Renault exhaust
family.gases
One ofwhile driving.isHowever,
the authors the owner their emissions
of an electric
have been
vehicle shifted
Renault Twizy,fromwhich
the exhaust pipe tobattery
has a traction the power withplant. This fact
a capacity of 6 is important
kWh. in the
The Renault
context of
Kangoo smog
small and other
delivery undesirable
vehicle phenomena
has a traction batteryoccurring especially
with a capacity inkWh.
of 45 cities.The
Electric
Re-
vehicles
nault Zoe,areone
theofmost
the ecological
best-selling when the energy
vehicles for charging
in Europe at the time,theirhad
traction batteries
batteries withcomes
a ca-
from renewable
pacity of 22 kWhenergy sources. of production and then 41 kWh. The Renault Megane E
at the beginning
An amount of 300 kWh
Tech car is a five-seater electric is the
SUV. energy
It hasneeded
a batteryto fully
with charge fourofbatteries
a capacity 40 and 60 of compact
kWh to
class electric vehicles. They are able to transport five people
choose from. However, the large Renault Master delivery vehicle has a traction battery over a distance of over
2000akm.
with It isofalso
capacity equivalent
40 or to 150% ofthe
87 kWh. Therefore, the energy
energy capacityduring
produced of theonetraction
day ofbattery
work
of an
can be electric
used tocitychargebus.several
This can
to atransport
dozen orapproximately
so vehicles from 75 zero
people to over a distance
full. There of
are, of
300 km. Therefore, even a small photovoltaic system is able to produce
course, vehicles with large battery capacities. An example would be a Tesla model S with significant amounts
aofbattery
energy,capacity
which enables
of over the100charged
kWh or vehicle
an Audifleet to cover
e-tron GT with considerable
a capacitydistances.
of over 90 kWh.
On-board chargers mounted in vehicles or external
Electric buses often have sets of traction batteries with a total energy chargers are used to charge
capacity vehicle
of over 200
traction batteries. The former are mobile converters of three-phase
kWh. For the latter vehicle fleets, PV systems with much higher peak powers should be AC power supplied
to the vehicle
considered thaninto
those thepresented
direct current
by theneeded
authorstoincharge the lithium-ion battery packs of
this article.
the vehicles. The latter are stationary devices supplying DC to vehicle traction batteries.
Charging
4.2. Chargingpoles or of
a Fleet wall boxesfrom
Vehicles thatRenewable
provide AC power
Energy to charge vehicles typically have
Sources
a power of 7, 11, or a maximum of 22 kW and are called slow battery charging systems.
Many people question the real ecology of electric vehicles [20]. When their batteries
Stationary DC chargers have powers ranging from 10 to 350 kW. DC chargers with powers
are charged with electricity generated in coal-fired power plants, they are not actually
from 50 kW are called fast battery charging systems. When using a DC charger, the battery
emission-free vehicles. They are emission-free vehicles only at the point of use because
they do not produce any harmful exhaust gases while driving. However, their emissions
have been shifted from the exhaust pipe to the power plant. This fact is important in the
context of smog and other undesirable phenomena occurring especially in cities. Electric
vehicles are the most ecological when the energy for charging their traction batteries
comes from renewable energy sources.
Energies 2024, 17, 1264 8 of 17

charging power depends on the power of the charger and the maximum power that can be
charged [52]. The press report shows that the latest electric Porsche Taycan has a battery
with a capacity of 105 kWh, which can be charged with a power of 320 kW [53]. Of course,
the battery charging power can be and is limited by the BMS battery management system,
but also by the charger itself and its operator [23]. This last function allows for a very
broad control of the vehicle battery charging process. The amount of energy needed to
charge a vehicle’s battery can be delivered faster using high power or more slowly using
lower power. The daily energy resource generated from renewable energy sources can
also be distributed among many vehicles. Vehicle batteries can always be fully charged
(state of charge, SoC = 100%) or quickly recharged to SoC = 80%. This is the limit value of
the SoC allowing charging at maximum power. Further charging (from SoC = 80 to 100)
takes place at lower power in order to protect the battery and extend the time of its proper
functioning. There are, of course, also battery types that can be charged with higher power
across a wider range of SoCs. Such batteries include lithium–titanium oxide (LTO) batteries.
The maximum charging and discharging rate for them is 10C [54]. LTO-based batteries also
have a wider operating temperature range and charging efficiency exceeding 98%.
The information presented above shows that the manager of an electric vehicle fleet can
make various choices regarding the size of batteries in vehicles and the methods of charging
them. Very often, one vehicle can be charged using both alternating current and direct
current. This is made possible by combined charging system (CCS) sockets and connectors.
Therefore, the biggest challenge is to provide an adequate amount of energy from
renewable sources to charge the batteries of the vehicle fleet. The price of fuel plays a
very large role in a vehicle’s total cost of ownership (TCO). In the case of electric vehicles,
this is the price paid per unit of energy. It may vary depending on the country and the
source of the electricity itself. RES have undergone and continue to undergo intensive
development in recent years, thanks to which the prices of components for the construction
of PV systems have significantly decreased. The return on investment in a PV system
in Poland is approximately 5 years without subsidies and less than 3 years in the case
of subsidies for investments from European Union funds. These are the authors’ own
calculations based on investments in PV systems in the Lublin Science and Technology
Park. This means nothing more than having an almost free source of electricity after the
payback period. Manufacturers and companies that assemble PVc systems currently offer a
25-year warranty on the operation of the main system components such as PV panels.
It is therefore justified to invest in new renewable energy generation capacity in
the form of photovoltaic systems dedicated specifically to charging fleets of electric ve-
hicles. It is worth emphasizing, however, that energy from PV systems constitutes only
part of the energy needed to charge vehicle batteries. Some of it must be taken from the
power grid, and regardless of its source (RES or coal), it will usually be much more expen-
sive than that produced by your own RES source [13]. Therefore, the task of the energy
manager in a company with a fleet of electric vehicles will be to appropriately select the
peak power of the photovoltaic system for the fleet of vehicles owned or planned to be
purchased. It is worth taking into account the fact that the shortest payback period for
investments in new renewable energy sources is characterized by investments with the high-
est auto-consumption rates. It means using as much energy as possible for your own needs.
It is usually unprofitable to feed excess energy produced into the power grid. The authors
propose selecting the appropriate peak power of the PV system to the energy demand of
the vehicle fleet in a tailor-made approach. This is best illustrated with a specific example,
which will be presented in the next chapter.

4.3. Modeling of Charging a Fleet of Electric Vehicles with Energy from Renewable Energy Sources
According to the authors, knowing the probability of producing a certain amount of
energy from PV systems in one day is key information necessary to plan and implement a
charging strategy for an electric vehicle fleet. The strategic model developed by the authors
will help with this.
Energies 2024, 17, 1264 9 of 17

In the third decade of the 21st century, almost all inverters in photovoltaic systems are
Internet of Things devices. This means that their work regarding the instantaneous power
produced and the energy generated over time is constantly monitored, and data regarding
the system’s operation are sent at regular intervals via wired or wireless transmission
methods to the data cloud. Then they can be processed, analyzed, and presented in the
form of useful charts supporting decision-making processes (business intelligence) in the
area of energy management.
Data on the monthly amount of energy produced were exported in digital form
and processed using specialized GeNIe 4.1 Academic software. First, the authors made
calculations for the month with the highest monthly energy production, i.e., May 2023
(Figure 4).
Basic and extended statistical calculations were made for the acquired data, as pre-
sented in Tables 1 and 2. The minimum value of energy produced monthly was 36,897 Wh,
the maximum value was 335,693 Wh, and the average value of energy produced was
247,558 Wh, with a standard deviation of 98,471.7 Wh. These data show that the daily
amount of electricity produced in Polish geographical conditions is characterized by high
variability in the month of May. The Metalog family of distributions allows for more
advanced statistical analysis including the determination of quantiles, as shown in Table 2.

Table 1. Statistical data on the amount of energy produced in the month of May (basic).

No. Parameter Value

1 Count 31
2 Minimum 36,897
3 Maximum 335,693
4 Mean 247,558
5 Std. Dev. 98,471.7

Table 2. Statistical data on the amount of energy produced in the month of May (extended).

No. Probability May

1 0.05 51,079
2 0.25 237,691
3 0.5 287,934
4 0.75 320,393
5 0.95 334,289
6 0.1612903225806 100,000
7 0.2258064516129 200,000

The GeNIe 4.0 Academic software allows you to determine the cumulative distribution
function (CDF) and probability density function (PDF) for various k coefficients (Figure 5).
The probability density function plot shows that high probability densities occur for large
daily amounts of energy generated. Therefore, in the spring months in Polish geographical
and climatic conditions, we can expect favorable conditions for the production of large
amounts of energy despite the still-short days. According to the authors, low air tempera-
ture has a very large impact on the production of the largest amount of energy of the year
in May. In summer months such as June, July and August, the sun is higher above the
horizon and shines much longer, but at much higher daily temperatures, which negatively
affects the amount of energy produced.
The next step in the analysis was to obtain information from the knowledge base.
The probability of daily energy production of 100,000 and 200,000 Wh was determined.
Obtaining information from the knowledge base is achieved by asking questions;
for example: What is the probability of monthly electricity production equal to or less
than 100,000 Wh by a PV system with a peak power of 50 kWp located in Lublin, Poland?
The question is asked by generating an additional row in the table shown in Table 2
and entering the number 100,000 in the right column. The system response is 0.1613.
Energies 2024, 17, x FOR PEER REVIEW 10 of 18

Energies 2024, 17, 1264 10 of 17

The GeNIe 4.0 Academic software allows you to determine the cumulative distribu-
tion function (CDF) and probability density function (PDF) for various k coefficients (Fig-
Therefore, the probability of producing more than 100,000 Wh of energy per month
ure 5). The probability density function plot shows that high probability densities occur
is 1 − 0.1613 = 0.8387. Questions can also be formulated regarding the probability of the
for large daily amounts of energy generated. Therefore, in the spring months in Polish
energy produced also amounting to 200,000 Wh. Therefore, the presented approach related
geographical and climatic conditions, we can expect favorable conditions for the produc-
to the use of the Metalog family of distributions can be used to simulate different energy
tion of largestrategies
generation amounts of forenergy despitedepending
PV systems the still-short days.
on the According
energy demandto the authors,
to charge low
a fleet
air temperature has a very large impact on the production of the largest amount
of electric vehicles. The results of the determined probability are presented in Table 3. of energy
of
Thethepresented
year in May. In summer
data show that in months such as June,
Polish geographical andJuly and August,
climatic the sun
conditions, is higher
a system with
above
a peakthe horizon
power and
of 50 kWpshines muchtolonger,
is likely but
be able to at much higher
produce daily
amounts of temperatures, which
electricity of 100,000
negatively
and 200,000 affects theday.
Wh per amount of energy produced.

Cumulativedistribution
Figure5.5.Cumulative
Figure distributionfunction
function(CDF)
(CDF)and
andprobability
probabilitydensity
densityfunction
function(PDF)
(PDF)for
forenergy
energy
produced by
produced by aa 50
50 kWp
kWpphotovoltaic
photovoltaicinstallation
installationin
inMay
May 2023.
2023.

Table 3. Probability of the amount of energy produced by a 50 kWp PV installation located in Poland.
The next step in the analysis was to obtain information from the knowledge base. The
probability of daily energy production of
Energy 100,000 and 200,000 Wh wasProbability
Probability determined.
Obtaining[Wh]
information from the knowledge ≤ base is achieved by asking> questions; for
example: What is the probability of monthly
100,000 electricity production equal
0.1613 to or less than
0.8387
100,000 Wh 200,000
by a PV system with a peak power 0.2258of 50 kWp located in Lublin,
0.7742Poland? The
question is asked by generating an additional row in the table shown in Table 2 and en-
teringThe
theauthors
numberspecifically
100,000 inproposed
the right to
column. The
take into systemthe
account response
amountsisof
0.1613.
energyTherefore,
produced
the
per day of 100 and 200 kWh in the calculations. This is due to the fact thatisthe
probability of producing more than 100,000 Wh of energy per month 1 −month
0.1613 in
=
2023 with the highest energy production was analyzed. The basic statistical data presented
Energies 2024, 17, 1264 11 of 17

in Table 1 show that the maximum value of energy produced per day this month exceeded
300 kWh. The authors recommend the use of stationary energy storage facilities in such
situations. Energy from RES will soon also be used to produce hydrogen for storage and
to power hydrogen fuel cell vehicles [21]. In this individual case, they propose using an
energy storage with an energy capacity of 100 kWh. It is worth considering purchasing a
new energy storage system using lithium iron phosphate technology (LFP) or giving new
life to used traction batteries from electric vehicles. In the latter case, these will usually be
lithium-ion batteries using NMC technology. An amount of 100 kWh is quite a large energy
capacity and will involve a large investment outlay. Therefore, such an energy storage
will not significantly reduce energy costs for electricity for charging electric vehicles, but it
will increase auto-consumption of the produced energy and protect the renewable energy
producer from additional fees for discharging energy into the grid at peak times. Moreover,
it is an excellent solution to protect against voltage failures in the power grid (blackout).
The proposed battery capacity is large enough to be 50% of the 200 kWh scenario and 100%
of the 100 kWh scenario. The energy collected in the warehouse can be used to charge fleet
vehicles in the evening or at night, i.e., when the photovoltaic system does not produce
energy. The energy storage can also be used to charge vehicles the next day. Both the
graph in Figure 4 and the course of the PDF in Figure 5 show that in the analyzed month
of May, days with a large amount of energy produced are followed by days with a very
small amount of energy produced. Therefore, energy storage gives the energy management
manager the choice of charging source for electric vehicles from batteries or from the
power grid. The energy storage also allows the vehicle fleet to be charged at night during
periods of lower electricity prices (special energy tariffs) and discharged during periods
of higher prices. The considerations presented above show that optimizing the process of
charging a vehicle fleet is a complicated issue that requires a complex infrastructure for
generating, storing, and transforming electricity. In this last area, it is worth mentioning
hybrid inverters, which are able to convert DC produced in a PV system into the AC needed
to power the power grid or into DC with the different voltages needed to charge an energy
storage unit or charge a vehicle battery. Modern hybrid inverters are complex devices with
many options for programming scenarios for charging and discharging energy storage.
In Polish geographical and climatic conditions, and taking into account the specific
location context of the analyzed photovoltaic system, similar results were obtained for
subsequent months of system operation. Figure 6 presents CDF and PDF for the energy
produced by a 50 kWp photovoltaic installation in July 2023. The monthly energy pro-
duction then amounted to 7.5 MWh. Expert analysis of the PDF provides information
about the high density of the probability distribution in the range of large amounts of
energy produced daily, ranging from 200 to over 300 kWh. However, the owner of a
strategic model using the Metalog family of probability distributions and the previously
mentioned GeNIe 4.1 Academic program does not have to have knowledge of the nu-
ances of producing electricity from renewable energy sources; the owner can directly ask
the knowledge base about the probability of producing a certain amount of energy in
a given month.
To better understand how the strategic model of charging vehicles with renewable
energy works, it is also worth considering the case of generating energy in months with
lower amounts of energy produced. An interesting example to analyze is the daily energy
production in October 2023. In Polish climatic and geographical conditions, it is the middle
of autumn. Basic statistical analysis informs us that a photovoltaic system with a peak
power of 50 kWp is able to produce over 100 kWh of energy in one day (Table 4). More
advanced statistics already determine that this amount of energy produced falls within the
probability percentiles of 0.75 and 0.95 (Table 5). By asking the knowledge base for the exact
probability value (Table 5, last row), we obtain the answer that the probability of achiev-
ing a daily energy production of more than 100 kWh this month is 1 − 0.6774 = 0.3226.
The probability of producing a daily amount of energy greater than 200 kWh is 0.
 energy produced daily, ranging from 200 to over 300 kWh. However, the owner of a stra-
tegic model using the Metalog family of probability distributions and the previously men-
tioned GeNIe 4.1 Academic program does not have to have knowledge of the nuances of
producing electricity from renewable energy sources; the owner can directly ask the
Energies 2024, 17, 1264 knowledge base about the probability of producing a certain amount of energy in a given
12 of 17
month.

Cumulativedistribution
Figure6.6.Cumulative
Figure distributionfunction
function(CDF)
(CDF)and
andprobability
probabilitydensity
densityfunction
function(PDF)
(PDF)for
forenergy
energy
produced by a 50 kWp photovoltaic installation in July 2023.
produced by a 50 kWp photovoltaic installation in July 2023.
Table 4. Statistical data on the amount of energy produced in the month of October (basic).
To better understand how the strategic model of charging vehicles with renewable
energy works,No.it is also worth considering the case of generating energyValue
Parameter in months with
lower amounts 1of energy produced. An interesting
Count example to analyze is the
31 daily energy
production in October
2 2023. In Polish climatic
Minimumand geographical conditions,12,791it is the mid-
dle of autumn. 3Basic statistical analysis informs
Maximum us that a photovoltaic system
139,447with a peak
power of 50 kWp 4 is able to produce over 100 MeankWh of energy in one day 78,951.5
(Table 4). More
5
advanced statistics already determine that Std. Dev.
this amount of energy produced36,056.3 falls within
the probability percentiles of 0.75 and 0.95 (Table 5). By asking the knowledge base for the
exact probability value (Table 5, last row), we obtain the answer that the probability of
Table 5. Statistical data on the amount of energy produced in the month of October (extended).

No. Probability October

1 0.05 23,052
2 0.25 49,366
3 0.5 82,626
4 0.75 112,014
5 0.95 133,549
6 0.6774193548387 100,000
Energies 2024, 17, 1264 13 of 17

Both the advanced statistical data presented in Table 5 and the PDF (Figure 7) show
that in the analyzed month, the system produces either very small amounts of energy of
the order of 10–50 kWh, or slightly larger amounts of 100–120 kWh. This is clearly visible
in the bimodal nature of the PDF (Figure 7). There are two local maxima for energies of
approximately 30 kWh and approximately 120 kWh. This means that we are either14
Energies 2024, 17, x FOR PEER REVIEW unable
of 18
to charge any electric vehicle with the energy produced or we are able to meet the scenario
of daily production of 100 kWh with a probability of 0.3226.

Figure 7.
Figure Cumulativedistribution
7.Cumulative distributionfunction
function(CDF)
(CDF)andandprobability
probabilitydensity
densityfunction
function(PDF)
(PDF)for
forenergy
energy
produced by
produced by aa 50
50 kWp
kWp photovoltaic
photovoltaic installation
installation in
in October
October 2023.
2023.

5. Discussion
5. Discussion
Using the strategic model for charging electric vehicles from renewable energy sources
Using the strategic model for charging electric vehicles from renewable energy
described in the previous sections, graphs of the probability of generating a daily amount
sources described in the previous sections, graphs of the probability of generating a daily
of energy of more than 100 and 200 kWh in the individual months of 2023 were calculated
amount of energy of more than 100 and 200 kWh in the individual months of 2023 were
and are presented in Figure 8. From the calculated probability values, it can be concluded
calculated and are presented in Figure 8. From the calculated probability values, it can be
that in Polish geographical climatic conditions, significant amounts of electricity can be
concluded that in Polish geographical climatic conditions, significant amounts of electric-
generated from a photovoltaic system with a peak power of 50 kWp. The input data for
ity can be generated from a photovoltaic system with a peak power of 50 kWp. The input
creating the strategic model comes from a specific photovoltaic system installed on the
data
roof for creating
of an the strategic
institutional model
building comes
in the city from a specific
of Lublin, photovoltaic
Poland. Thus, thesystem
model installed
includes
on the roof of
geographic an institutional
context. building
The strategic in the
model alsocity of Lublin,
includes the Poland. Thus,context
engineering the model in-
related
cludes geographic context. The strategic model also includes the engineering context
to the type, azimuth, and inclination angle of the installed photovoltaic panels. In this re-
lated to the type, azimuth, and inclination angle of the installed photovoltaic panels. In
this complex context, a photovoltaic system is able to generate an amount of energy
greater than 100 kWh every day between March and September with a high probability
of over 0.7. In the months from May to September, it is able to generate amounts of energy
greater than 200 kWh but with a probability of over 0.5. In the following months, from
 Energies 2024, 17, 1264 14 of 17

complex context, a photovoltaic system is able to generate an amount of energy greater than
100 kWh every day between March and September with a high probability of over 0.7.
In the months from May to September, it is able to generate amounts of energy greater
Energies 2024, 17, x FOR PEER REVIEWthan 200 kWh but with a probability of over 0.5. In the following months, from November 15 of 18
to January, the system is unable to generate a daily amount of energy produced greater
than 100 kWh. In the autumn and winter months, the amounts of energy produced daily
are too small to charge the batteries of the vehicle fleet. Based on the strategic model in
in question, the vehicle fleet charging manager is able to calculate the probability of the
question, the vehicle fleet charging manager is able to calculate the probability of the photo-
photovoltaic system
voltaic system producing
producing specific
specific amounts
amounts of electricity
of electricity and initially
and initially determine
determine theof
the share
share of green energy in the total energy mix needed to charge the
green energy in the total energy mix needed to charge the vehicle fleet. vehicle fleet.

Figure
Figure8. 8.
Graphs of the
Graphs probability
of the of generating
probability a daily
of generating amount
a daily of energy
amount of more
of energy than 100
of more thanand
100200
and
kWh in individual months of 2023.
200 kWh in individual months of 2023.

Theaccuracy
The accuracyofofthe themathematical
mathematicalmodel modelininthe thestrategic
strategicmodel
modelfor forcharging
chargingelectric
electric
vehicles from RES increases with the amount of data
vehicles from RES increases with the amount of data entered. Energy production dataentered. Energy production data
fromseveral
from severalyears
yearsofofoperation
operationofofthe thePV PVsystem
systemincreases
increasesthe theaccuracy
accuracyofofthetheprobability
probability
calculation.Due
calculation. Duetotothethehighhighquality
qualityofofthe theproduced
producedPV PVpanels
panelsand andthe
thevery
verysmall
smallannual
annual
degradationofoftheir
degradation theirperformance,
performance,ititcan canbebeassumed
assumedthat thatthethepresented
presentedmodel
modelcan canbebeused
used
throughoutthe
throughout thelife
lifeofofthethePV
PVsystem.
system.OfOfcourse,course,it itisisnot
notnecessary
necessarytotointroduce
introducea astrategic
strategic
elementrelated
element related to thethe degradation
degradationofofthethe photovoltaic
photovoltaic system’s
system’sperformance
performance into the
intomodel.
the
It will be reflected in the data regarding the amount of energy
model. It will be reflected in the data regarding the amount of energy produced in the produced in the subsequent
years of the
subsequent system’s
years of theoperation. The strategic
system’s operation. model based
The strategic model onbased
actualonmeasurement
actual measure- data
fromdata
ment PV systems
from PVallows
systems us allows
not only ustonotestimate
only towith accuracy
estimate withthe probability
accuracy distribution
the probability
of the amount
distribution of energy
of the amountproduced
of energyby the photovoltaic
produced system per system
by the photovoltaic day; it can
per also
day;be used
it can
to detect weather anomalies and diagnose the correct operation
also be used to detect weather anomalies and diagnose the correct operation of the entire of the entire PV system.
PVWhat is important
system. in the areainofthe
What is important thearea
latest market
of the latest trends
market it that theitapproach
trends presented
that the approach
by the authors can be used in a fully automatic way in a system
presented by the authors can be used in a fully automatic way in a system for managing for managing the energy
the energy produced from RES, both for charging vehicles and for simply supplying aor
produced from RES, both for charging vehicles and for simply supplying a residential
institutional
residential building with
or institutional electricity.
building withDue to the use
electricity. Dueof to
Bayesian
the usenetworks
of Bayesian to operate
networks the
toGeNIe
operate 4.1the
Academic
GeNIe 4.1 program,
Academic it fits into theittrend
program, fits intoof using artificial
the trend intelligence
of using artificialmethods
intelli-
(AI) to support business decisions (business intelligence).
gence methods (AI) to support business decisions (business intelligence).
6. Conclusions
6. Conclusions
Based on their own experience with charging electric vehicles from renewable energy
Based on their own experience with charging electric vehicles from renewable energy
sources, the authors developed a strategic model for charging electric vehicles from renew-
sources, the authors
able energy sources.developed
Due to the aorigin
strategic
of themodel foranalysis,
data for chargingtheelectric
modelvehicles
takes intofrom re-
account
newable energy sources. Due to the origin of the data for analysis, the model
the geographical and climatic context related to the location of the photovoltaic system takes into
account
itself, asthe geographical
well and climatic
as the engineering context
context relatedrelated
to the to theazimuth,
type, location and
of the photovoltaic
inclination angle
system itself, as well as the engineering context related to the type, azimuth, and inclina-
tion angle of the installed photovoltaic panels. The model uses the Metalog probability
distribution family to calculate the probability that a 50 kWp peak photovoltaic system
will produce a given amount of electricity per day. This energy can be used to charge the
traction batteries of a fleet of electric vehicles. Based on calculations from the strategic
model, we can conclude that the tested photovoltaic system is able to generate more than
Energies 2024, 17, 1264 15 of 17

of the installed photovoltaic panels. The model uses the Metalog probability distribution
family to calculate the probability that a 50 kWp peak photovoltaic system will produce
a given amount of electricity per day. This energy can be used to charge the traction
batteries of a fleet of electric vehicles. Based on calculations from the strategic model, we
can conclude that the tested photovoltaic system is able to generate more than 100 kWh of
energy every day in the months from March to September with a high probability of over
0.7. In the months from May to September, it is able to generate amounts of energy greater
than 200 kWh but with a probability of over 0.5. In the following months, from November
to January, the system is unable to generate a daily amount of energy produced greater
than 100 kWh. In the autumn and winter months, the amounts of energy produced daily
are too small to charge the batteries of the vehicle fleet. The presented strategic model may
have practical application in systems for managing electricity produced from renewable
energy sources. Based on the strategic model in question, the manager of the charging
of the electric vehicle fleet is able to calculate the probability of the photovoltaic system
producing specific amounts of electricity and initially determine the share of green energy
in the total energy mix needed to charge the vehicle fleet. The strategic model of charging
electric vehicles from renewable energy sources is part of the trend of using AI methods to
support business decisions (business intelligence).
The authors specifically selected a photovoltaic system with a peak power of 50 kWp
in order to easily scale the system to several MWp. The authors intend to continue the
research they have started to complicate the model and increase its accuracy. They also
plan to include the use of a stationary energy storage facility in the future model, which
will allow for an increase in the self-consumption rate of energy produced from renewable
energy sources.

Author Contributions: Conceptualization, J.C. and A.M.; methodology, A.M.; software, A.M.; val-
idation, J.C., A.M. and B.Š.; formal analysis, B.Š.; investigation, A.M.; resources, J.C. and A.M.;
data curation, A.M.; writing—original draft preparation, J.C., A.M. and B.Š.; writing—review and
editing, J.C., A.M. and B.Š.; visualization, A.M.; supervision, J.C.; project administration, B.Š.;
funding acquisition, J.C. and A.M. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data are contained within the article.
Conflicts of Interest: The authors declare no conflicts of interest.

Abbreviations
AC alternating current
CCS combined charging system
CDF cumulative distribution function
DC direct current
LFP lithium iron phosphate (LiFePO4)
LTO lithium-titanium-oxide
NMC nickel manganese cobalt
PDF probability density function
PV photovoltaic
RES renewable energy sources
SoC state of charge
TCO total cost of ownership

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