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Citation: de Carvalho Pinheiro, H.
PerfECT Design Tool: Electric Vehicle
Modelling and Experimental
Validation. World Electr. Veh. J. 2023,
14, 337. https://doi.org/10.3390/
wevj14120337
Academic Editor: Joeri Van Mierlo
Received: 2 November 2023
Revised: 27 November 2023
Accepted: 30 November 2023
Published: 5 December 2023
Copyright: © 2023 by the author.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
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4.0/).
Article
PerfECT Design Tool: Electric Vehicle Modelling and
Experimental Validation
Henrique de Carvalho Pinheiro
Department of Mechanical and Aerospace Engineering (DIMEAS), Politecnico di Torino, 10138 Turin, Italy;
henrique.decarvalho@polito.it
Abstract:
This article addresses a common issue in the design of battery electric vehicles (BEVs)
by introducing a comprehensive methodology for the modeling and simulation of BEVs, referred
to as the “PerfECT Design Tool”. The primary objective of this study is to provide engineers and
researchers with a robust and streamlined approach for the early stages of electric vehicle (EV) design,
offering valuable insights into the performance, energy consumption, current flow, and thermal
behavior of these advanced automotive systems. Recognizing the complex nature of contemporary
EVs, the study highlights the need for efficient design tools that facilitate decision-making during
the conceptual phases of development. The PerfECT Design Tool is presented as a multi-level
framework, divided into four logically sequential modules: Performance, Energy, Currents, and
Temperature. These modules are underpinned by sound theoretical foundations and are implemented
using a combination of MATLAB/Simulink and the vehicle dynamics software VI-CRT. The research
culminates in the validation of the model through a series of experimental maneuvers conducted
with a Tesla Model 3, establishing its accuracy in representing the mechanical, electrical, and thermal
behavior of BEVs. The study’s main findings underscore the viability of the design tool as an asset in
the initial phases of BEV design. Beyond its primary application, the tool holds promise for broader
utilization, including the development of active control systems, advanced driver assistance systems
(ADAS), and solutions for autonomous driving within the domain of electric vehicles.
Keywords:
electric vehicles; modelling and simulation; design methodology; vehicle dynamics;
electric powertrain; batteries
1. Introduction
The electric vehicle is not a 21st century invention. At the beginning of the automotive
industry in the early 1900s, three main architectures dominated the automobile market:
40% were steam powered, 38% were electric and just 22% used gasoline [
1
]. Electric vehicles
were seen as a very convenient solution since they were quiet, did not suffer from vibrations
or fumes, and the engines, unlike those that needed to be cranked, required little effort
to start.
These advantages were counterposed by some limitations related to their range (no
higher than 50–65 km), maximum speed (limited to around 30 km/h), and the length of
time to recharge. It is easy to find similarities to the current challenges of EVs.
For that reason, after a short period of market success, especially in urban settings,
electric vehicles were practically completely substituted by the ICE of Benz and, soon after,
the ubiquitous Model T from Ford. For decades, the EV market was almost null, apart from
special applications and some very punctual examples [2].
Interest in the technology gained momentum in the 1990s, with many examples of mass
market proposals and big players, such as General Motors, announcing their intentions
to produce new electric models [
3
]. An important driver for this revival was regulatory,
with the first version of the Zero-Emission Vehicles (ZEV) mandate being announced in
California [4].
World Electr. Veh. J. 2023,14, 337. https://doi.org/10.3390/wevj14120337 https://www.mdpi.com/journal/wevj
World Electr. Veh. J. 2023,14, 337 2 of 28
Indeed, the importance of the EV movement from the beginning of the 21st century
is twofold: technological and regulatory. If, from one side, key technologies like lithium
batteries started to be applied to vehicles and greatly improved EV performance [
5
,
6
], from
the other side, the restrictions imposed by policy are a constant pressure for the quick
development of such technologies.
The European emission standards directives are among the most important initiatives
for pollution control in the mobility sector. Since 1992, when the Euro 1 standard was put in
place [
7
], a continuous effort to restrict the amount of emissions from vehicles has become
part of the European scenario, leading to many other similar regulations around the world.
The trend created by the European Commission continues until today, with ever higher
levels of constraint on emissions. Euro 7 is expected by 2025 [
8
] and programs like the “Fit
for 55” [
9
] promise severe limitations on ICE vehicles in the European market, including a
possible 100% CO
2
emissions reduction by 2035 [
10
], making it virtually impossible for big
carmakers to ignore the electrification tendency.
The future of the EV market looks bright, with the favorable legislation push creating
demand for zero-emission vehicles at the same time that technologies like batteries continue
to increase their performance and see their prices drop [
11
]. Most business reports and
market analyses put the estimates of market growth in the vicinity of 20% CAGR [
12
,
13
],
mostly concentrated in the Chinese, European and US markets.
This outlook does not come, of course, without a series of challenges. The recycling of
batteries [
14
–
16
], safety [
17
,
18
], recharging times and limitations of the grid [
19
–
21
], scarcity
of key-materials [
22
] and energy consumption for manufacturing [
23
] are important threats.
The work presented in [
24
] analyzes whether or not this automotive solution will be
able to maintain its title as the main personal form of mobility, or meet the challenge of
achieving the “six zero goals” of Zero Emissions, Zero Energy, Zero Congestion, Zero Acci-
dent, Zero Empty, and Zero Cost. The authors forecast that new evolutions in technology
can help the sector to sufficiently evolve.
It is important to evaluate the overall impact of new forms of mobility, not just in
terms of local pollutants or overall emissions, but with a broader approach. This kind of
analysis can be performed with LCA (Life Cycle Assessment) tools, as shown in [
25
]. This
work proposes a sound methodology for vehicle impact evaluation and concludes that,
even with a power mix dominated by fossil fuel strategies, EVs can be effective in reducing
gas emissions in the overall LCA.
New technologies are emerging in terms of energy storage, and electrochemical sources
continue to promise evolution and performance improvements [
26
–
30
] beyond the current
levels of the market [
6
]. New technologies and chemistries such as lithium air [
31
], lithium-
sulphur [
32
,
33
], sodium superoxide [
34
,
35
] and solid-state [
36
–
38
] are promising solutions,
but are not yet ready to be deployed in the market. Other sources of energy [
39
–
41
] and the
continuous effort to reduce mass [
42
–
49
] and increase energy efficiency [
50
–
52
] also work
towards a more electrified future.
In the current scenario for the automotive field, the competition is always fiercer, both
because of the creation of huge sector empires (through the mergers and acquisitions of big
players) and due to the pressure of new entrants from emerging markets. These pressures
create, more than ever, the necessity to reduce the time-to-market of new models and to
trim all possible wastes (of time and money) during the development phases.
Engineering digital tools are not new in the sector, and they play a crucial role in
today’s vehicle development. It is unthinkable to produce even a first prototype of a
component without several loops of Computational Aided Design (CAD), Computational
Aided Engineering (CAE), and Computational Fluid Dynamics (CFD) and the use of many
other specialized tools. It is natural that during the evolution of the product development
workflow, these tools are used to support the process change.
It is no secret that vehicle development is a complex task; among the many different
subsystems and their often interdependent and complex relations, it must be considered
also the not-so-clear subjective evaluations and needs of the different users. A car must
World Electr. Veh. J. 2023,14, 337 3 of 28
have high power, but low fuel consumption; it must be spacious, but aerodynamically
streamlined; it must be beautifully shaped, but its bodywork must be easily manufacturable;
it must have the most advanced technologies but the price must be affordable. Designing a
vehicle is as much an art as it is engineering.
These compromises are as true for EVs as they are for ICE vehicles. One main differ-
ence, though, is the timing of these two vehicle technologies: ICE vehicles were born and
gained popularity at the beginning of the XX century, a period with a much less globalized
and complex economy and much less technology at the disposal of designers and engineers.
The methods used for the development of the first ICEVs cannot be the same as those used
to create this new batch of automobiles.
A classic approach to product development is the so-called V-model [
53
], in which
the workflow begins with broad-view requirements analysis and performance definition
at then vehicle level, then moves to the design and definition of the architectures and
solutions at the sub-system level and finally to the implementation phase, in which the
specific characteristics of the components are defined.
This first “leg” of the V-shape incrementally increases the level of detail and the special-
ization level requested. At the end of the product definition and execution, the validation
stages begin, where the final product will be compared to the initially defined performance
targets. This phase happens in a reverse order, from the requirement verification of the
single components to the sub-systems, to the full-vehicle validation. Clearly this process is
not linear, meaning that every time a performance is not met during the validation phase,
or a problem is noticed in the component design phase, it can be necessary to loop back to
the previous stages to adjust and adapt them accordingly.
This V-shape approach with design loops can generate problems and delays in the
launch workflow, especially when big gaps in performance are outlined in the very final
phases of testing. More modern strategies tend to include verification phases earlier on
in the process to reduce the impact of the changes and expedite the development using
approaches such as the Multiple V-model and incremental V-model [
53
]. However, the
general philosophy of narrowing down and specializing during the design, then building
up and increasing integration in the validation phase is still in place.
Following this framework, what is necessary, in terms of simulation and design tools,
to support EV development?
It is clear from the workflow that the level of specialization and detail increases with
time. It is also true that the single components of an E-PWT already possess (apart, maybe,
from batteries) a plethora of instruments to support their development. Arguably, the most
pressing challenges occur at the beginning of the design process.
One might think that the concept phases of the engineering process are an easier task
than the implementation, however this stage is full of uncertainties and plays a critical role
in the success of a new endeavor. At the very start, it is usual not to have a clear picture of
vehicle layout, feasibility, and overall performance attainable. Making choices in this kind
of environment is undoubtedly hard, thus having a support tool becomes handy. Such a
tool must be sufficiently precise and at the same time cannot depend on a full set of vehicle
parameters, still being studied, and decided.
This article presents multi-level process for modelling and design of electric vehi-
cles, entitles “PerfECT Design Tool”. More specifically, the design tool is divided into
four independent but logically sequential modules (Performance, Energy, Current and
Temperature–motivating the acronym), whose theoretical base and implementation details
are presented in the following sessions. After laying out the structure of the tool, a practical
application and experimental validation campaign are presented, featuring the case study
of a Tesla Model 3.
The main contribution of the article is the logic and method proposed for the stream-
lined design process of new electric vehicles, specifically regarding the first phases of
the product development process, always keeping in mind that for each component or
subsystem there are dedicated tools and methods that run in parallel. Apart from this,
World Electr. Veh. J. 2023,14, 337 4 of 28
other uses are also envisioned; for example, the method can be used as a platform for the
design of active control systems [
54
–
58
], ADAS and autonomous driving [
59
,
60
] solutions
for EVs. The novelty of the solution is its multi-step nature, modularity, and flexibility of
implementation which, in comparison with commercial tools, can offer a more tailored
experience to professionals working on different phases of the design process.
The article will show the modelling theoretical background used for the development
in Section 2, the actual implementation of the model in its various stages in Section 3and
the experimental validation of the algorithm in Section 4.
2. Modelling Theoretical Background
This session briefly presents some of the essential models used that are related to: the
lateral dynamics of vehicles, handling, and stability; longitudinal dynamics, drivability
and energy efficiency; the main components of electric powertrains, namely batteries and
electric motors; and finally, the thermal phenomena taking place in EVs such as heat
generation, and heat transfer.
2.1. Lateral Dynamics Modelling
Vehicle dynamics is a branch of automotive engineering that aims to describe the
responses of automobiles when performing maneuvers. The history of vehicle dynamics as
a consolidated branch of scientific inquiry begins with motorsports. The need to push the
limits of racecars and improve their performance during challenging track competitions
obliged engineers to formally study the physical phenomena behind vehicle dynamics, in
addition to the “trial and error” method that was once the main approach. As a matter of
fact, the clear objectives and rigid restrictions of racing provide an excellent framework for
understanding vehicle behavior, as extensively shown by Milliken in their textbook [61].
When it comes to lateral behavior, arguably the most relevant study regards the
controllability of the vehicle by means of steering inputs. The steering wheel is the main
interface between driver and automobile; thus, it becomes essential to establish the response
dynamics for each driving condition.
Commonly, when describing the most elementary models of lateral dynamics, the
vehicle is represented by a reduced version of the four-wheel layout, in which left and
right-hand sides are collapsed in the so-called “bicycle model” (Figure 1). This single-
track approach allows for a leaner description and less cumbersome equations, without
significantly jeopardizing accuracy.
World Electr. Veh. J. 2023, 14, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/wevj
application and experimental validation campaign are presented, featuring the case
study of a Tesla Model 3.
The main contribution of the article is the logic and method proposed for the stream-
lined design process of new electric vehicles, specifically regarding the first phases of the
product development process, always keeping in mind that for each component or sub-
system there are dedicated tools and methods that run in parallel. Apart from this, other
uses are also envisioned; for example, the method can be used as a platform for the design
of active control systems [54–58], ADAS and autonomous driving [59,60] solutions for
EVs. The novelty of the solution is its multi-step nature, modularity, and flexibility of im-
plementation which, in comparison with commercial tools, can offer a more tailored ex-
perience to professionals working on different phases of the design process.
The article will show the modelling theoretical background used for the development
in Section 2, the actual implementation of the model in its various stages in Section 3 and
the experimental validation of the algorithm in Section 4.
2. Modelling Theoretical Background
This session briefly presents some of the essential models used that are related to: the
lateral dynamics of vehicles, handling, and stability; longitudinal dynamics, drivability
and energy efficiency; the main components of electric powertrains, namely batteries and
electric motors; and finally, the thermal phenomena taking place in EVs such as heat gen-
eration, and heat transfer.
2.1. Lateral Dynamics Modelling
Vehicle dynamics is a branch of automotive engineering that aims to describe the
responses of automobiles when performing maneuvers. The history of vehicle dynamics
as a consolidated branch of scientific inquiry begins with motorsports. The need to push
the limits of racecars and improve their performance during challenging track competi-
tions obliged engineers to formally study the physical phenomena behind vehicle dynam-
ics, in addition to the “trial and error” method that was once the main approach. As a
matter of fact, the clear objectives and rigid restrictions of racing provide an excellent
framework for understanding vehicle behavior, as extensively shown by Milliken in their
textbook [61].
When it comes to lateral behavior, arguably the most relevant study regards the con-
trollability of the vehicle by means of steering inputs. The steering wheel is the main in-
terface between driver and automobile; thus, it becomes essential to establish the response
dynamics for each driving condition.
Commonly, when describing the most elementary models of lateral dynamics, the
vehicle is represented by a reduced version of the four-wheel layout, in which left and
right-hand sides are collapsed in the so-called “bicycle model” (Figure 1). This single-track
approach allows for a leaner description and less cumbersome equations, without signif-
icantly jeopardizing accuracy.
Figure 1. The bicycle model vehicle diagram [62].
Figure 1. The bicycle model vehicle diagram [62].
By defining the front and rear forces developed in the tires as linear relations with
α
through the tire stiffness coefficients C
F
and C
R
, it is relatively easy to establish the relation
between
δ
and the other parameters defining the lateral motion (lateral acceleration a
y
,
World Electr. Veh. J. 2023,14, 337 5 of 28
curvature radius R, yaw rate
γ
and vehicle sideslip
β
), which are relevant when reproducing
their final form. The explicit equations can be written in an elegant, reduced form:
Mz=Iz
.
r=Nββ+Nrr+Nδδ(1)
Fy=mV(r+.
β) = Yββ+Yrr+Yδδ(2)
taking advantage of the concept of “Derivative Notation”. As the name suggests, the terms
N
β
,N
r
,N
δ
,Y
β
,Y
r
, and Y
δ
bundle the relevant physical parameters of the vehicle, directly
defining the partial derivative of
.
r
and
.
β
with respect to each vehicle state (sidelip angle
and yaw rate) or control state (steering angle). The values of the derivatives are defined as:
Yβ=dFy
dβ=(CF+CR),Nβ=dMz
dβ=(aCF−b CR)
Yr=dFy
dr =1
V(aCF−bCR),Nr=dMz
dr =1
Va2CF+b2CR)
Yδ=dFy
dδ=−CF,Nδ=dMz
dδ=−aCF
(3)
The most convenient and compact way to represent the dynamic equations is the state
space matrixial approach. Considering the decoupling between lateral and longitudinal
dynamics, it is possible to write the same set of equations as
.
x=Ax +Bu (4)
where
x=β
γ,A=
Cf+Cr
mvx
aC f−bCr
mvx2−1
aC f−bCr
Iz
a2Cf+b2Cr
Izvx2
,u=δ
Mz,B= −Cf
mvx0
−aC f
Iz
1
Iz!(5)
The “bicycle model” is a simple, interesting, and very insightful means to study
the macro-behavior of a vehicle; however, its precision and robustness are limited. One
common method to increase model complexity resides in the use of a multibody dynamics
approach. However, at the very beginning of the design process of a vehicle, it is difficult
to obtain all the information necessary to develop a full-vehicle multibody model.
To reduce both the complexity of the data inputs, and computational effort, a simpler
version of the multibody system can be used. Instead of describing each mechanical
component separately, and writing all six equations of motion, a reduced mechanical
system can be created, in which only five elements are included: the vehicle body and
the four wheels. This model, called the “Isolated Vehicle” in the textbook by Genta and
Morello [
63
], considers one of the mechanical elements (usually the vehicle body) as
the main body with a full six degrees-of-freedom (DOF) motion description, while the
secondary bodies present only the “free” DOF after considering their relationship with
the main body in terms of joints. More specifically, in a passenger vehicle, the body has
6 DOF and each one of the wheels has, at least, one DOF with respect to the body (the
wheel travel).
Following the approach suggested by [
63
], the steps required to derive the equations
of motion of the system are the computation of potential and kinetic energies, the virtual
work of external forces, and the dissipation function followed by the definition of the
equations of motion using Lagrange equations.
Regarding the suspension system, whilst it is not described by analytical kinematic
relations (as in the multibody models) it is necessary to describe its motion—more specifi-
cally, the relative displacements of the wheels and body. The motion can be described as
a function of the generalized coordinate
ζ
that represents the wheel travel distance. The
motion in each direction of the general coordinate system can be written as a function of
ζ
and, therefore, interfaced with the rest of the equations. Each suspension arrangement
will, thus, have a particular expression to represent its kinematics. In software solutions
World Electr. Veh. J. 2023,14, 337 6 of 28
such as VI-CRT 2022 [
64
], it is possible to derive the curves representing the kinematic
relations beforehand (by importing kinematic models from multibody software, by using
their proprietary toolbox or manually inserting the desired diagrams) so that the tables are
consulted to solve the numerical systems.
2.2. Longitudinal Dynamics Modelling
The main sources of resistance to the vehicle’s motion are aerodynamic drag, tire rolling
resistance, grade force, and transmission losses. Apart from the resistances themselves, it is
also convenient to model the inertial effects to describe the longitudinal accelerations.
The
aerodynamic drag
represents the force generated by the resistance associated
with the movement of the vehicle through the air. The most common way to represent such
force is in
Raero =1
2ρV2
rSCx(6)
where
ρ
is the air density,
V2
r
is the longitudinal velocity of the vehicle relative to the
air (considering the xcomponent of the wind), Sis the vehicle’s front area and
Cx
is the
drag coefficient.
The
rolling resistance
is a phenomenon that occurs when the tires are in motion. The
elastomeric material in contact with the road will deform at the entrance of the contact
patch and relax after sliding out of the contact zone, but all the energy used to compress
the material will not be recovered, thus creating dissipation [65].
The energy necessary to overcome the tire deformation can be interpreted as a force,
whose moment counterposes the forward movement of the wheel, either slowing it down
or requesting an active torque from the powertrain to keep a constant speed. The rolling
resistance is not easy to describe analytically, and it is usual to represent it as this experi-
mental curve
Rroll =Fzf0+kV2(7)
where
f0
,
k
, are experimental coefficients,
Fz
is the vertical load acting on the wheel, and
V
is the longitudinal speed. It is important to highlight that the vertical force acting on the
vehicle will vary depending on the slope and aerodynamic effects. This approach is very
convenient, since it incorporates all resistance effects related to the rolling motion, such as
the bearing friction and the aerodynamic resistance generated by the rolling wheels, even if
minor, with respect to the deformation effect.
The
grade force
is the component of the resistance to motion of a vehicle that depends
directly on the slope of the road. More specifically, it is the projection of the vehicle’s weight
in the direction parallel to the road:
Rgrad =m·g·sin(α)(8)
where αis the road slope.
Transmission losses
are not properly a resistance force, in the sense that they form
an internal resistance that is usually modeled as an efficiency
ηt
associated with the
motor outputs:
Preal =ηt·Pmotor (9)
The efficiency includes the contribution of gearbox, differential, shafts, bearings,
hook joints, clutches and all other components connecting the motors to the wheel hubs.
For electric vehicles, when single-gear setups are chosen, the number of components
on the drivetrain are drastically reduced, as is their complexity and contribution to the
overall efficiency. This efficient value can be assumed as fixed for a first analysis of the
transmission system.
To properly calculate the accelerations of the vehicle, it is also necessary to consider
the inertial contribution of spinning masses. Using an energetic approach, an expression
World Electr. Veh. J. 2023,14, 337 7 of 28
of the “equivalent mass”
me
can be written from the relationship between the rotational
speeds and the vehicle speed:
me=m+Jwheel
R2
e
+Jtrans
R2
eτ2
f
+Jmotor
R2
eτ2
fτ2
g
(10)
where
Jwheel
,
Jtrans
and
Jmotor
are the moments of inertia of wheels, transmission, and motor
respectively;
Re
is the effective wheel radius; and
τf
and
τg
are the final and gearbox
transmission ratios.
Knowing the external forces acting upon the vehicle, it is possible to describe its
motion in the longitudinal direction:
m.
V=Fx1+Fx2+Fxaer −m·g·sin(α)
0=Fz1+Fz2+Fza er −m·g·cos(α)
−m·hCG ·
.
V=Fz1a−Fz2b+m·g·hCG·sin(α)−Maer +Fxaer hCG
(11)
Fz1=mg
l·hbcos(α)−hCGsin(α)−ρS
2mg CxhCG −CMyl+bCzV2−hCG
g
.
Vi
Fz2=mg
l·hacos(α)+hCGsin(α)−ρS
2mg −CxhCG +CMyl+aCzV2+hCG
g
.
Vi(12)
2.3. Batteries
Side-by-side with the electric drive, the batteries are the core element of the E-PWT.
Energy storage is a key part of the performance of EVs, determining their maximum
capabilities in terms of power output and, at the same time, the range and total capacity of
the EV [66].
Typical automotive batteries are composed of assemblies of battery cells, representing
the basic electrochemical unit of the system. The cells are then grouped and connected
in modules, which are connected to create the overall battery pack. To achieve targets of
voltage and capacity, the cells and the modules are connected in series or in parallel.
The most widespread choice is the latter, namely using the Thévenin equivalent circuit
approach. Typically, models use single or double polarization (meaning one or two RC
blocks after the resistance R0) as in Figure 2.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 2 of 14
efficiency. This efficient value can be assumed as fixed for a first analysis of the trans-
mission system.
To properly calculate the accelerations of the vehicle, it is also necessary to consider
the inertial contribution of spinning masses. Using an energetic approach, an expression
of the “equivalent mass” can be written from the relationship between the rotational
speeds and the vehicle speed:
=+
+
+
(10)
where , and are the moments of inertia of wheels, transmission, and mo-
tor respectively; is the effective wheel radius; and and are the final and gearbox
transmission ratios.
Knowing the external forces acting upon the vehicle, it is possible to describe its mo-
tion in the longitudinal direction:
=++
−∙∙()
0=++−∙∙()
−∙ℎ∙=−+∙∙ℎ∙()−+ℎ
(11)
⎩
⎪
⎨
⎪
⎧
=
∙()−ℎ
sin()−
2
ℎ
−
+
−ℎ
=
∙()+ℎsin()−
2−ℎ++
+ℎ
(12)
2.3. Batteries
Side-by-side with the electric drive, the batteries are the core element of the E-PWT.
Energy storage is a key part of the performance of EVs, determining their maximum ca-
pabilities in terms of power output and, at the same time, the range and total capacity of
the EV [66].
Typical automotive batteries are composed of assemblies of battery cells, represent-
ing the basic electrochemical unit of the system. The cells are then grouped and connected
in modules, which are connected to create the overall battery pack. To achieve targets of
voltage and capacity, the cells and the modules are connected in series or in parallel.
The most widespread choice is the latter, namely using the Thévenin equivalent cir-
cuit approach. Typically, models use single or double polarization (meaning one or two
RC blocks after the resistance R0) as in Figure 2.
Figure 2. Dual polarization Thévenin circuit for electrochemical cell [67].
It is possible to directly derive the overall module/pack equivalent Thévenin circuit
(composed of Ns identical cells in series and Np identical cells in parallel) by computing
their parameters R0, R1, R2, C1 and C2 with straightforward arithmetic:
,=
∙,, , =
∙,
(13)
Figure 2. Dual polarization Thévenin circuit for electrochemical cell [67].
It is possible to directly derive the overall module/pack equivalent Thévenin circuit
(composed of N
s
identical cells in series and N
p
identical cells in parallel) by computing
their parameters R0,R1,R2,C1and C2with straightforward arithmetic:
Ri,eq =Ns
Np
·Ri,cell,Ci,eq =Np
Ns
·Ri,cell (13)
From the analysis of the response of the Thévenin circuit under different currents,
it is possible to describe an important phenomenon related to the discharge rates. The
faster the charge/discharge, the lower the efficiency of the cell and, thus, the lower the
apparent capacity.
World Electr. Veh. J. 2023,14, 337 8 of 28
2.4. Electric Powertrain
In order to represent the motor’s working principles and obtain the equations relating
to the electric values, magnetic values, and the mechanical output, it is possible to approach
the problem in a generalized approach as proposed in [
68
]. This kind of approach explores
the electromagnetic relations using generalized reference systems with transformation
matrixes to adapt the various possible forms of construction and arrangement of the EM.
Performing the transformation to the d–qaxis with Clarke–Park transforms, one can
find the general for equation for the voltages in matrix form as:
Vd
Vq=RsId
Iq+d
dt λd
λq+ω0−1
1 0 λd
λq(14)
While the expression for the fluxes becomes
λd
λq=LdLdq
Lqd Lqid
iq+λmd
λmq (15)
The terms of magnetization
λmd
and
λmq
and the inductances
Ld
,
Lq
,
Ldq
and
Lqd
,
depend on the specific type of PM machine studied and on the overall modeling hypothesis.
For example:
•
In the case of SPM machines, the disposition of the magnets in the rotor is isotropic,
thus the terms
Ld=Lq
, while the flux generated by the PMs is aligned with the d-axis
so λmd =λmwhile λmq =0;
•
For IPM the situation is equivalent regarding the PM flux, but the disposition of the
PM is anisotropic, and made so that Ld>Lq;
•
In the case of RM, the form of the rotor is such that the contribution of the inductances
is much more influential in the d-axis, thus
LdLq
, while no PM is included, so that
λmd =λmq =0;
•
For PM–SyR machines it remains true that
LdLq
; however, the presence of PMs in
the structure means that the contribution is λmq =−λmwhile λmd =0.
Typical EM power and torque phases are represented as Figure 3. The first phase
is represented by a constant maximum torque output (limited by the maximum current
allowed) followed by a constant power phase (where the limit voltage also plays an
important role) making the torque see a hyperbolic reduction with speed increments.
Maximum rotational speed (due to maximum frequency) determines the limit EM speed–
which could also be caused by mechanical limits, although not common.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 3 of 14
From the analysis of the response of the Thévenin circuit under different currents, it
is possible to describe an important phenomenon related to the discharge rates. The faster
Figure 3. Typical torque and power curves for EMs [67].
2.5. Thermal Modelling
In EVs there are tighter limits of temperature so that the core components of the E-
PWT can work properly.
Electric motors usually can endure temperatures as high as 140 °C in their coils, after
which problems with electronic components or demagnetization of the PMs can occur and
permanently damage the electric machine.
Power electronics also require close attention to heat generation and temperature
management. Dealing with high currents and important switching frequencies, the prob-
lem of overheating is critical. The range of temperatures for which semi-conductors or
other internal components in the inverters can deteriorate is similar to those of EMs, in
the order of 150–175 °C.
Batteries, on the other hand, work with even more challenging constraints. The most
suitable range of temperatures for Li-ion cells is between 15 °C and 35 °C. There are three
main components contributing to the heat generation: motors, inverters, and batteries.
In Ems, there are four principal sources of heat: copper losses, iron losses, aerody-
namic drag, and mechanical friction. For the purposes of modeling, it will be assumed
that all energy associated with internal losses are converted, directly or indirectly, into
heat.
Copper losses, also referred to as ohmic losses, this kind of loss is related to the re-
sistance in the windings and is directly related to the currents flowing in the EM. For syn-
chronous machines, only the stator contributes to the power:
==3
(16)
where Rs is the phase winding resistance and Iph is the current flowing in each phase.
For induction machines the stator term is similar, but the rotor contribution must be in-
cluded:
=+ = 3
+ 3
(17)
Iron losses are related to the electromagnetic fluxes passing through the ferromag-
netic materials. There are two main mechanisms, namely, hysteresis and eddy currents.
The power related to the hysteresis Phys follows the expression:
=∙∙
(18)
being proportional to the EM frequency f and with the square of the flux intensity B and
the constant Chys that encompasses the material specific behavior.
Figure 3. Typical torque and power curves for EMs [67].
The models aim to describe the EMs without an explicit implementation of the low-
level control of the electric machines, which would entail an unfeasibly large computational
World Electr. Veh. J. 2023,14, 337 9 of 28
burden [
69
]. To accomplish this goal, the electro-mechanical features of the EMs are defined
through the application of the MTPA principle. By solving the optimization problem and
finding the combination of
id
and
iq
that simultaneously outputs the desired torque and
minimizes the total absorbed current, it is possible to reasonably estimate the outcomes
of a properly designed low-level control without explicit modelling. Specifically, in the
case of the presented model, the MTPA-based results are encapsulated into look-up tables
calculated a priori, since the chosen approach depends on the fixed resistance, reluctance,
and magnetization parameters (instead of varying maps) [
70
]. This proves to accelerate
considerably the simulation process.
2.5. Thermal Modelling
In EVs there are tighter limits of temperature so that the core components of the E-PWT
can work properly.
Electric motors usually can endure temperatures as high as 140
◦
C in their coils, after
which problems with electronic components or demagnetization of the PMs can occur and
permanently damage the electric machine.
Power electronics also require close attention to heat generation and temperature
management. Dealing with high currents and important switching frequencies, the problem
of overheating is critical. The range of temperatures for which semi-conductors or other
internal components in the inverters can deteriorate is similar to those of EMs, in the order
of 150–175 ◦C.
Batteries, on the other hand, work with even more challenging constraints. The most
suitable range of temperatures for Li-ion cells is between 15
◦
C and 35
◦
C. There are three
main components contributing to the heat generation: motors, inverters, and batteries.
In Ems, there are four principal sources of heat: copper losses, iron losses, aerodynamic
drag, and mechanical friction. For the purposes of modeling, it will be assumed that all
energy associated with internal losses are converted, directly or indirectly, into heat.
Copper losses
, also referred to as ohmic losses, this kind of loss is related to the
resistance in the windings and is directly related to the currents flowing in the EM. For
synchronous machines, only the stator contributes to the power:
Pco pper =PRs =3RsI2
ph (16)
where R
s
is the phase winding resistance and I
ph
is the current flowing in each phase. For
induction machines the stator term is similar, but the rotor contribution must be included:
Pco pper =PRs +PRr =3RsI2
ph +3RrI2
r(17)
Iron losses
are related to the electromagnetic fluxes passing through the ferromagnetic
materials. There are two main mechanisms, namely, hysteresis and eddy currents. The
power related to the hysteresis Phys follows the expression:
Phys =Chys·B2·f(18)
being proportional to the EM frequency fand with the square of the flux intensity Band
the constant Chys that encompasses the material specific behavior.
Regarding the eddy currents, an expression to estimate the eddy currents’ dissipated
power is:
Peddy =Ceddy·B2·f2(19)
Usually hysteresis effects, eddy currents’ dissipated power, and other secondary loss
mechanisms associated with magnetic flow are experimentally determined and represented
by the Steinmetz equation that sums up the effect with three coefficients k,mand nto fit
the EM response [71]:
Piron =k·Vc·fm·Bn(20)
World Electr. Veh. J. 2023,14, 337 10 of 28
Aerodynamic losses
(or windage losses) represent the mechanical power dissipation
due to the interaction of the EM rotor and the air gap between the rotor and stator. This
phenomenon is highly dependent on the shape of the rotor and stator in the surfaces close
to the air gap, and also to the rotation velocity. In the case of a cylindrical shape (very
common for EMs) the coefficient
Caero
shall be proportional to the air density
ρ
, to the
radius rof the rotor to the power of four, and to the length of the rotor L:
Pwindage =Caero ·ω3→Caero ∝ρ,r4,L(21)
Friction losses
are a second type of mechanical loss, due to the friction occurring in
the mechanical interfaces of the motor, the most important of which occurs in the bearings.
Neglecting other contributions due to gaskets or other sealing components, the bearing
friction can be calculated using the methodologies suggested by the manufacturers, such as:
Tbearing =1
2µdP
P=XkrFr+YkaFa(22)
where
µ
is the friction coefficient determined by the type of bearing, dis the bearing
diameter, Xand Yare the radial and axial load factors (informed by the manufacturer), kr
and
ka
are the dynamic load related to the operation conditions, and
Fr
and
Fa
are the loads
acting on the bearing in the radial and axial directions.
In practice, instead of computing all the single contributions to the EM power loss, the
most widespread form to represent them is by using a lumped model in which the iron
losses, windage losses and friction losses are put together after an experimental evaluation.
Another interesting approach that can be followed to estimate the EM losses, following a
similar theoretical modeling of the single contributions is found in [
72
], where a strategy of
scaling is used to translate a reference efficiency map into an unknown new map from a
single-point analysis.
In
batteries
, there are two main mechanisms of heat generation: internal resistance
and chemical reactions.
•Internal resistance
: with the current flows in the battery pack, it is possible to deter-
mine the resistance contribution to the total energy loss and consequent heat genera-
tion. In the case of a constant current discharge, the heat generated can be expressed as:
Qbatt =(uOC −ub)·ib(23)
Using the more general approach of the Thévenin equivalent circuit to represent the
battery cells (and by extension the modules/pack) it can be determined that the heat
generated in the batteries follows:
Qbatt =R0i2
b+R1i2
1+R2i2
2(24)
•Chemical reactions:
as is known, during the release or absorption of energy from/to
the battery, chemical reactions take place. Apart from the electric equilibrium that
represents the main mechanism of the chemical battery, these reactions also play a
role in terms of heat generation. The heat associated with the chemical reaction can be
derived by:
Qchem =T·∆SI
−1·F→∆S=−1·F∂ub
∂T(25)
where
Qchem
represents the heat related to the chemical reaction, Tis the temperature,
∆S
the entropy variation, Ithe current, Fis the Faraday constant and ubis the voltage.
Note that the direction is opposite in charge and discharge, so the heat generation will
follow, making it exothermic during discharge and endothermic during charge, differently
from the resistance heat, always increasing temperature of the cell in both directions.
World Electr. Veh. J. 2023,14, 337 11 of 28
Very complex models can be put in place to estimate the heat generation in the
inverter
.
A possible approach is to divide the losses between switching losses and ohmic losses due
to currents flowing in the circuit. For the purposes of this work, the detailed functioning of
the inverter is out of scope, and its modeling is limited to its overall efficiency under the
observed conditions.
To be more precise on the effects of the inverter efficiency on the powertrain output
power and on the heat generation, it is possible to substitute the fixed efficiency
ηinv
with a
fixed value for each quadrant of operation (forward/backward vs. accelerating/braking),
or even creating a look-up table with discretized values of efficiency, whenever these values
are available.
Once the various heat sources are known and modeled, it is essential to understand
how this heat flows across the components of the E-PWT, how its exchange influences the
temperature of the parts, and, finally, how much of the heat is extracted by the cooling
system and dissipated by the ambient air.
The modeling strategy chosen to tackle the heat transfer problem is the so-called circuit
equivalence model (Figure 4).
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 4 of 14
Figure 4. Thermal–electric equivalence [73].
Taking advantage of this strategy, the thermal values are compared to electric equiv-
alents, in order to describe the system response: The current I on the electric system is
equivalent to the heat transfer Q; the temperature difference between two bodies Δ is
compared to the voltage; and the electric resistance becomes a thermal resistance .
By using this analogy, the basic heat transfer phenomena of conduction and convection
can be uniformly modeled as the equation:
=Δ
(26)
The main difference between each specific heat transfer condition will lay, therefore,
in the strategy used to calculate the value of . The complexity related to geometry is
then removed from the main equation and passed on to its inherent coefficient.
3. The PerfECT Design Tool Implementation
3.1. The Four-Level Concept
The key concept of the developed methodology is the modularity of each of the four
design steps. Each of the four levels proposed has increasing complexity and considers
different phases of the product development, always regarding the concept and initial
design stage. The four levels are: Performance, Energy, Currents and Temperature (thus
composing the acronym PerfECT). The levels were derived from an analysis of the natural
order of the development of vehicles. In detail:
Performance level: this level reflects the very beginning of the conceptual study of
the vehicle, in which the only readily available information and “fixed” features are
the ones decided in the requirements definition and registered in the product require-
ment document. This stage then focuses on the “reality check” of the desired perfor-
mance, an evaluation of possible layouts for the powertrain, and a first broad pro-
curement phase on E-PWT components, more specifically at this stage in terms of
electric machines. It naturally follows that, in such an analysis, only the very essential
vehicle parameters can be requested, and only very simple outcomes can be reliably
expected;
Energy level: as with the previous step, the energy level proposes a simple and quick
modeling structure, focusing on the longitudinal dynamics response of the vehicle and
adding information regarding the energy flow. When it comes to energy evaluation, the
main additional information provided to the system are the curves of the e-motors
Figure 4. Thermal–electric equivalence [73].
Taking advantage of this strategy, the thermal values are compared to electric equiv-
alents, in order to describe the system response: The current Ion the electric system is
equivalent to the heat transfer Q; the temperature difference between two bodies
∆T
is
compared to the voltage; and the electric resistance
Relec
becomes a thermal resistance
Rth
.
By using this analogy, the basic heat transfer phenomena of conduction and convection can
be uniformly modeled as the equation:
Q=∆T
Rth
(26)
The main difference between each specific heat transfer condition will lay, therefore,
in the strategy used to calculate the value of
Rth
. The complexity related to geometry is
then removed from the main equation and passed on to its inherent coefficient.
3. The PerfECT Design Tool Implementation
3.1. The Four-Level Concept
The key concept of the developed methodology is the modularity of each of the four
design steps. Each of the four levels proposed has increasing complexity and considers
different phases of the product development, always regarding the concept and initial
World Electr. Veh. J. 2023,14, 337 12 of 28
design stage. The four levels are:
Perf
ormance,
E
nergy,
C
urrents and
T
emperature (thus
composing the acronym PerfECT). The levels were derived from an analysis of the natural
order of the development of vehicles. In detail:
•Performance level
: this level reflects the very beginning of the conceptual study
of the vehicle, in which the only readily available information and “fixed” features
are the ones decided in the requirements definition and registered in the product
requirement document. This stage then focuses on the “reality check” of the desired
performance, an evaluation of possible layouts for the powertrain, and a first broad
procurement phase on E-PWT components, more specifically at this stage in terms of
electric machines. It naturally follows that, in such an analysis, only the very essential
vehicle parameters can be requested, and only very simple outcomes can be reliably
expected;
•Energy level
: as with the previous step, the energy level proposes a simple and
quick modeling structure, focusing on the longitudinal dynamics response of the
vehicle and adding information regarding the energy flow. When it comes to energy
evaluation, the main additional information provided to the system are the curves of
the e-motors (usually available from suppliers’ datasheet) and information regarding
battery capacity, energy management and the regenerative braking strategy. From this
analysis, it is possible to extract some vital features for EVs, such as their expected
range, and therefore also adjust parameters to increase/optimize them;
•Currents level
: the gap between the energy level and currents level is probably the
widest among the sequences; in order to successfully evaluate currents flowing in
the high-voltage circuits of an E-PWT, it is necessary to significantly increase the
complexity of the electric machine modeling and their correlated components. From
this level on, the lateral dynamics simulation platform is also optionally integrated, in
such a way that the designer can expand the analysis from pure drivability to include
handling and stability analyses;
•Temperature level
: as the final stage of the concept phase in product development,
this level adds an important number of parameters to the analysis related to thermal
characteristics. To correctly evaluate the temperature variations on the vehicle com-
ponents, it is essential to understand the heat generation, heat transfer, and cooling
loop features; each one of these is based on several hypotheses and parameters. The
goal of the tool is not to substitute specialized thermal modeling software; therefore, a
geometry-less approach was used in which the physical disposition and connections
among parts is represented by lumped thermal exchange resistances. This approach
allows for the PerfECT tool to be used as a target-setting instrument and as an interface
with detailed CFD and multi-physics analysis.
It is evident that the use of the design tool does not encompass all the technical
challenges and disciplines in vehicle development. The PerfECT design tool alone does not
tackle aspects solely related to vehicle dynamics (such as suspension design), or the many
other design aspects related to structural analysis, NVH, external aerodynamics, etc.
3.2. Performance Level
Figure 5shows the main interface of the model and relevant input parameters.
At this level, it is possible to choose the speed profile and slope value/map to be fol-
lowed, at the left-hand side. Then, the main block “Cycle and vehicle model” encompasses
both the driver action and vehicle longitudinal response. The outputs are motor speed,
motor torque, and wheel torque. The other blocks use the data to create suitable plots and
output all relevant quantities, such as vehicle speed, EM power, resistive power, distance,
and wheel/EM torques. Figure 6shows the subsystem.
World Electr. Veh. J. 2023,14, 337 13 of 28
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 13 of 28
3.2. Performance Level
Figure 5 shows the main interface of the model and relevant input parameters.
Figure 5. Performance level: main Simulink model view (top) and parameter input mask (bottom).
At this level, it is possible to choose the speed profile and slope value/map to be fol-
lowed, at the left-hand side. Then, the main block “Cycle and vehicle model” encompasses
both the driver action and vehicle longitudinal response. The outputs are motor speed,
motor torque, and wheel torque. The other blocks use the data to create suitable plots and
output all relevant quantities, such as vehicle speed, EM power, resistive power, distance,
and wheel/EM torques. Figure 6 shows the subsystem.
Figure 5. Performance level: main Simulink model view (top) and parameter input mask (bottom).
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 6 of 14
Figure 6. Performance level: cycle and vehicle model.
This level comprises four main areas:
Blue: calculates the maximum traction that the tires can transmit to the road due to
the friction coefficient, mass, slope, and longitudinal load transfer (hCG and accelera-
tion);
Yellow: compares the actual speed and the target in the desired profile and chooses
the adequate wheel torque request using a PI controller;
Red: receives the saturated torque request and calculates the resistive torque based
on the vehicle speed, thereby obtaining the residual acceleration, and integrating it
to obtain the next timestep velocity;
Green: recalls and calculates the block outputs—motor angular speed, wheel torque
and motor torque.
The presented blocks sum up the main features of the “Performance” level. Using
this model, it is possible to perform some analysis:
WOT acceleration: by imposing a very high target velocity from the beginning of the
simulation, it is possible to determine the time evolution of speed under maximum
torque request. The acceleration is limited by EM features, friction, inertia, and resis-
tive forces, which can be tuned and tweaked to achieve design goals as 0–100 km/h
time;
Maximum slope: by interactively increasing the slope angle input, it is possible to
analyze the vehicle response on design criteria such as maximum gradeability or
minimum speed/acceleration in pre-determined slope conditions;
Maximum speed: it is possible to numerically determine the maximum speed achiev-
able by the vehicle. Like the WOT analysis, it can be done by setting a high value of
target speed and forcing the system to give all available power/torque in such a way
that the speed will tend to the maximum obtainable value. The limit can be due to
torque/power of the EM being counterposed by the resistances or due to a motor
speed limit;
Residual acceleration: at any given operation point, the system can be used to eval-
uate the total resistive power and compare it with the peak values of the powertrain
to determine the available residual power that can be exploited for acceleration.
Figure 6. Performance level: cycle and vehicle model.
World Electr. Veh. J. 2023,14, 337 14 of 28
This level comprises four main areas:
•Blue
: calculates the maximum traction that the tires can transmit to the road due to the
friction coefficient, mass, slope, and longitudinal load transfer (h
CG
and acceleration);
•Yellow
: compares the actual speed and the target in the desired profile and chooses
the adequate wheel torque request using a PI controller;
•Red:
receives the saturated torque request and calculates the resistive torque based
on the vehicle speed, thereby obtaining the residual acceleration, and integrating it to
obtain the next timestep velocity;
•Green:
recalls and calculates the block outputs—motor angular speed, wheel torque
and motor torque.
•
The presented blocks sum up the main features of the “Performance” level. Using this
model, it is possible to perform some analysis:
•WOT acceleration
: by imposing a very high target velocity from the beginning of the
simulation, it is possible to determine the time evolution of speed under maximum
torque request. The acceleration is limited by EM features, friction, inertia, and resistive
forces, which can be tuned and tweaked to achieve design goals as 0–100 km/h time;
•Maximum slope
: by interactively increasing the slope angle input, it is possible to
analyze the vehicle response on design criteria such as maximum gradeability or
minimum speed/acceleration in pre-determined slope conditions;
•Maximum speed
: it is possible to numerically determine the maximum speed achiev-
able by the vehicle. Like the WOT analysis, it can be done by setting a high value
of target speed and forcing the system to give all available power/torque in such a
way that the speed will tend to the maximum obtainable value. The limit can be due
to torque/power of the EM being counterposed by the resistances or due to a motor
speed limit;
•Residual acceleration:
at any given operation point, the system can be used to evalu-
ate the total resistive power and compare it with the peak values of the powertrain to
determine the available residual power that can be exploited for acceleration.
3.3. Energy Level
The second level of the analysis is very similar to the previous in terms of the layout of
the simulation model. As a matter of fact, the main difference is found in the input strategy
of the EM features.
Instead of inputting maximum torque and maximum power as fixed singular values,
at the “Energy” level it is possible to include torque and power curves. The method used to
permit such inputs is the use of Look-Up Tables (LUT). By translating the power and torque
curves into discretized tables, the LUT blocks in Simulink 2023aallow for the interpolation
of intermediate points to obtain dynamic saturation limits for the simulation.
Of course, apart from the torque and power data, the energy level requires a reference
to EM efficiency. In this case, the input data for the model are in the form of discretized
curves. By supplying the model with 2D tables of efficiency varying with load and speed,
it is possible to dynamically consult the LUT to determine the instantaneous efficiency and,
thus, estimate the real energy required to complete the vehicle mission.
Apart from the features of the EM, more detailed when input as tables, the other
big difference on the “Energy” level regards the presence of the battery capacity. The
model does not simulate the electric response per se, but estimates the discharge depth
by scaling the total pack capacity (calculated by multiplying the cell capacity by the total
number of cells) with the requested energy from the E-PWT. In this case, a new saturation
is included regarding the maximum power output of the battery, that can potentially limit
the acceleration and regeneration.
Finally, the last difference regards the modeling of the regenerative behavior. Once
the energy outcome is decided upon, it is important to know the amount of energy to be
recovered through the action of the EMs.
World Electr. Veh. J. 2023,14, 337 15 of 28
3.4. Currents Level
Figure 7shows its main interface.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 7 of 14
3.3. Energy Level
The second level of the analysis is very similar to the previous in terms of the layout
of the simulation model. As a matter of fact, the main difference is found in the input
strategy of the EM features.
Instead of inputting maximum torque and maximum power as fixed singular values,
at the “Energy” level it is possible to include torque and power curves. The method used
to permit such inputs is the use of Look-Up Tables (LUT). By translating the power and
torque curves into discretized tables, the LUT blocks in Simulink 2023aallow for the inter-
polation of intermediate points to obtain dynamic saturation limits for the simulation.
Of course, apart from the torque and power data, the energy level requires a reference
to EM efficiency. In this case, the input data for the model are in the form of discretized
curves. By supplying the model with 2D tables of efficiency varying with load and speed,
it is possible to dynamically consult the LUT to determine the instantaneous efficiency
and, thus, estimate the real energy required to complete the vehicle mission.
Apart from the features of the EM, more detailed when input as tables, the other big
difference on the “Energy” level regards the presence of the battery capacity. The model
does not simulate the electric response per se, but estimates the discharge depth by scaling
the total pack capacity (calculated by multiplying the cell capacity by the total number of
cells) with the requested energy from the E-PWT. In this case, a new saturation is included
regarding the maximum power output of the battery, that can potentially limit the accel-
eration and regeneration.
Finally, the last difference regards the modeling of the regenerative behavior. Once
the energy outcome is decided upon, it is important to know the amount of energy to be
recovered through the action of the EMs.
3.4. Currents Level
Figure 7 shows its main interface.
Figure 7. Currents level: main Simulink interface.
In the reported scheme, a version of the model with two independent motors is im-
plemented, represented by the two subsystems at the right. Both blocks communicate with
the Battery block (in orange at the top-left corner) by sending their power requests, and
with the vehicle dynamics block by supplying the driveline torques generated. Another
torque input comes from the “Mechanical Brakes” subsystem.
The vehicle dynamics block (in green at center-left position) can be used in two dif-
ferent modes: the first is very similar to the interfaces in the “Performance” and “Energy”
levels, modeling only the longitudinal response of the vehicle through the mask’s
Figure 7. Currents level: main Simulink interface.
In the reported scheme, a version of the model with two independent motors is
implemented, represented by the two subsystems at the right. Both blocks communicate
with the Battery block (in orange at the top-left corner) by sending their power requests,
and with the vehicle dynamics block by supplying the driveline torques generated. Another
torque input comes from the “Mechanical Brakes” subsystem.
The vehicle dynamics block (in green at center-left position) can be used in two dif-
ferent modes: the first is very similar to the interfaces in the “Performance” and “Energy”
levels, modeling only the longitudinal response of the vehicle through the mask’s parame-
ters; the second is where the vehicle response is simulated using the co-simulation option
with VI-CRT. Apart from these “mechanical model” blocks (green) and electric model
blocks (orange), two other “logic” blocks are implemented (yellow):
•Control Unit
: this subsystem is responsible for translating the input desired speed
profile and transforming it into a torque request to the E-PWT and mechanical brakes.
It encompasses, basically, the PI controller and the regenerative braking controller
from the “Energy” level. The main difference, in this case, is that the “Motor Torque
Reference Generator”, responsible for the translation of 0–100% acceleration signals
into torques, considers the saturations coming from different sources. The torque
limits, power limits and speed limits come from the signals in the EM models, taking
into consideration not only the peak or continuous values present in the EM datasheets,
but also the logic of over-torque, over-power and over-speed and their maximum
allowable times;
•Energy management system:
this subsystem is responsible for translating the total
torque request coming from the controller into a torque command for each motor in
the E-PWT. The first step is to perform further saturation, by inquiring the maximum
power and voltage available at the battery level (Figure 8).
This procedure is conducted by means of a bisecting algorithm that iteratively predicts
the necessary currents to fulfill the demand, and, using the battery data, calculates the
tension drop and final power. Once this step is concluded, the torque allocation logic can
be implemented.
World Electr. Veh. J. 2023,14, 337 16 of 28
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 8 of 14
parameters; the second is where the vehicle response is simulated using the co-simulation
option with VI-CRT. Apart from these “mechanical model” blocks (green) and electric
model blocks (orange), two other “logic” blocks are implemented (yellow):
Control Unit: this subsystem is responsible for translating the input desired speed
profile and transforming it into a torque request to the E-PWT and mechanical
brakes. It encompasses, basically, the PI controller and the regenerative braking con-
troller from the “Energy” level. The main difference, in this case, is that the “Motor
Torque Reference Generator”, responsible for the translation of 0–100% acceleration
signals into torques, considers the saturations coming from different sources. The
torque limits, power limits and speed limits come from the signals in the EM models,
taking into consideration not only the peak or continuous values present in the EM
datasheets, but also the logic of over-torque, over-power and over-speed and their
maximum allowable times;
Energy management system: this subsystem is responsible for translating the total
torque request coming from the controller into a torque command for each motor in
the E-PWT. The first step is to perform further saturation, by inquiring the maximum
power and voltage available at the battery level (Figure 8).
Figure 8. Currents level: energy management system.
This procedure is conducted by means of a bisecting algorithm that iteratively pre-
dicts the necessary currents to fulfill the demand, and, using the battery data, calculates
the tension drop and final power. Once this step is concluded, the torque allocation logic
can be implemented.
With the physical data and MTPA maps [70], the EM blocks are responsible for trans-
forming the torque requests into effective torque outputs and determining the currents
and power necessary to do so. The main systems inside the block are:
Inverter: converts the torque request into output Vd and Vq signals and motor status,
after saturating the torque request with the maximum flux, available voltage, and
Figure 8. Currents level: energy management system.
With the physical data and MTPA maps [
70
], the EM blocks are responsible for trans-
forming the torque requests into effective torque outputs and determining the currents and
power necessary to do so. The main systems inside the block are:
•Inverter
: converts the torque request into output V
d
and V
q
signals and motor status,
after saturating the torque request with the maximum flux, available voltage, and
information regarding the overloads. Using the MTPA maps this block converts
reference EM torque into I
d
and I
q
minimum currents to achieve such torque, then
through the physical model they are used to determine the voltages;
•Overload management
: is composed of three smaller blocks, each one responsible
for keeping track of one of the following key overload behaviors: Torque, Power and
Speed. The overload state is characterized by an output that lies between the continuous
reference and the peak reference. Obviously, it is not possible for the EM to maintain
a peak performance indefinitely, so these controllers determine when to return to the
continuous value after some time in overload. The method used to do so is based on a
“StateFlow” module in Simulink, where an energetic approach is implemented. The
basic idea is that each instant the system is over the continuous value, it is accumulating
energy that will then be turned into heat and compromise long-term performance. Once
the energy level is too high—based on supplier indications—StateFlow takes it back to
the continuous level until the accumulated heat has not dissipated. The same outline is
used for the three overload behaviors;
•Motor electro-mechanical model
: this block is a straightforward implementation
of the equivalent circuit equations in the d-q axis EM model. From them, the real
output torque can be calculated, modeling the internal fluxes and EM dynamics.
The electromagnetic power needed to perform this operating point load can also
be determined;
•Driveline
: the last block determines the share of the power that shall not be available
to create useful mechanical torque, due to internal losses and inefficiencies (as well as
the extra power requested to the storage system). Here, the copper losses, iron losses,
bearing losses, aerodynamic losses, and inertial counter-torque are estimated.
World Electr. Veh. J. 2023,14, 337 17 of 28
Regarding the battery simulation, the main block is the “Battery pack”, where the
Thévenin equivalent circuit model equations are implemented and solved, then the battery
current and voltage is determined for that power level.
The current then is inputted in the “SOC Estimator” that implements a Coulomb
counting strategy to determine the depth of discharge imposed and therefore integrate it to
define the new SOC. The SOC level will, in the next time step, define the internal battery
parameters and change the features of the equivalent circuit itself.
The third block in this subsystem regards the BMS. Keeping in mind that the name
Battery Management System can refer to much more complex systems, this block is re-
sponsible for putting the system into “Protection” mode if the minimum SOC is achieved,
and to make sure the requested currents, voltages and power are compatible with the
battery limitations.
3.5. Temperature Level
The last level of the PerfECT tool adds a new layer to the “currents” level, meaning that
the calculations previously performed do not depend on the results obtained by thermal
analysis, but are essential to their calculation. It is possible, however, to use the LUT
input method to create system features that vary with the temperature, creating a full
closed-loop model.
For the EM thermal analysis, each component (Stator, Rotor, Shaft, End Caps, Casing,
and Internal Air in the cavity) is separately considered. Inside the blocks, each one of
the thermal exchanges among these components is described by establishing a thermal
resistance coefficient, as well as the setup of the mass and thermal capacity of the part.
Although it is difficult to gather all the necessary data in a reliable way, this approach
allows for quite a simple modeling strategy.
A similar procedure is performed to model the inverters, which are divided into
sub-components (chips, baseplate, heat sink and pack’s air) and each one receives a series
of parameters to describe the heat exchange and temperature variations throughout the
simulation. The same exact logic is valid for the battery, where the cells, pack and internal
air are modeled as independent and connected elements; the heat generated follows the
previously discussed mechanisms (Equations (24) and (25)).
Apart from the exchange among components, when suitable, the part can exchange
heat with the cooling fluid and with the external environment. The fluid is then circulated
among the components, following the actual (or desired) physical arrangement. The
cooling circuit counts with a radiator, which is responsible for the heat dissipation. It is,
however, possible to avoid the modeling of the actual heat exchanger by imposing a fixed
temperature for the fluid at the beginning of the loop—corresponding to a situation in
which the radiator is capable of completely reducing the fluid temperature to that of the
one of the environments, i.e., an ideal (or over-dimensioned) heat exchanger.
Apart from the “tricky” thermal resistances that rule the internal heat exchanges in
the single parts and between components and the cooling system, some other factors must
be inputted in the model:
•Ambient temperature;
•Initial temperature of each part;
•Cooling fluid volume, density and heat capacity;
•Radiator dimensions and efficiency;
•Cooling circuit flow rate and distribution among components.
It is, arguably, true that the precise definition of all the thermal features beforehand
(especially without access to the design or experimental tests) is an unfeasible task; however,
the “Temperature” level of the PerfECT tool presents itself as a great tool for supporting
design teams when the project approaches the system design and component selection.
Imagine a cooling designer that can set the targets for her heat exchangers, pumps, and the
fluid itself, not by experience, trial-and-error, or by looking at benchmarking examples, but
by testing the effects of each choice in the predicted temperature variations of the system.
World Electr. Veh. J. 2023,14, 337 18 of 28
The possibility of running sensitivity analyses and optimizations without the compu-
tational burden often associated with CFD or multi-physics software has huge potential.
4. Practical Validation on a Tesla Model 3
In this section the modelling strategy will be implemented and validated with a real-
m[use case. The application in a real vehicle case study serves not only as an example, but
as the basis for a well-needed experimental validation of the methodology.
4.1. The Vehicle
The vehicle chosen for the case study is the Tesla Model 3, specifically, the 2021 Tesla
Model 3 Long-Range AWD. This vehicle represents one of the most popular and widespread
BEVs on the market. Table 1shows some of the basic geometric and inertial parameters of
the vehicle.
Table 1. Tesla Model 3 main dimensions and mass parameters.
Parameter Value Unit
wheelbase 2875 mm
track 1580 mm
mass LF 517 kg
mass RF 505 kg
mass LR 530 kg
mass RR 518 kg
total mass 2070 kg
unsprung mass front 22.7 kg
unsprung mass rear 19.5 kg
sprung mass 1985.6 kg
CoG x 1419 mm
CoG y 18 mm
CoG z 468 mm
Ixx 2.65 ×108kg ×mm2
Iyy 1.04 ×109kg ×mm2
Izz 1.69 ×109kg ×mm2
Ixy 3.22 ×106kg ×mm2
Ixz 4.14 ×107kg ×mm2
Iyz 4.15 ×105kg ×mm2
The overall dimensions and masses were easy to obtain. The inertias were estimated
from reference values present in software databases [
64
] and scaled to match the specific
model. The CoG height (Z coordinate) was harder to assess. One widespread technique,
adopted in this case, is the modified reaction method (MRM) [74–76].
The aerodynamic data of the Tesla Mode 3 can be found in Table 2.
World Electr. Veh. J. 2023,14, 337 19 of 28
Table 2. Tesla Model 3 main aerodynamic features.
Parameter Value Unit
Air density 1.225 kg/m3
Frontal area 2.22 m2
Drag coefficient (Cx) 0.23 -
Lift coefficient (Cz) 0.09 -
CoP distribution 0.5 -
The Tesla Model 3 battery pack, more specifically the Long-Range version taken into
consideration, is composed of four modules, as shown in Figure 9.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 19 of 28
sprung mass 1985.6 kg
CoG x 1419 mm
CoG y 18 mm
CoG z 468 mm
Ixx 2.65 × 108 kg × mm2
Iyy 1.04 × 109 kg × mm2
Izz 1.69 × 109 kg × mm2
Ixy 3.22 × 106 kg × mm2
Ixz 4.14 × 107 kg × mm2
Iyz 4.15 × 105 kg × mm2
The overall dimensions and masses were easy to obtain. The inertias were estimated
from reference values present in software databases [64] and scaled to match the specific
model. The CoG height (Z coordinate) was harder to assess. One widespread technique,
adopted in this case, is the modified reaction method (MRM) [74–76].
The aerodynamic data of the Tesla Mode 3 can be found in Table 2.
Table 2. Tesla Model 3 main aerodynamic features.
Parameter Value Unit
Air density 1.225 kg/m3
Frontal area 2.22 m2
Drag coefficient (Cx) 0.23 -
Lift coefficient (Cz) 0.09 -
CoP distribution 0.5 -
The Tesla Model 3 battery pack, more specifically the Long-Range version taken into
consideration, is composed of four modules, as shown in Figure 9.
Figure 9. Tesla Model 3 unassembled battery pack.
Each of the modules is composed of cylindrical cells disposed in series and parallel.
As can be seen, the two modules on the outer edges of the pack are smaller than the other
two central ones. This is not only a geometric placement difference, but a change in the
number of cells. As a matter of fact, the external modules are composed of 1058 cells while
the internal ones have 1150 units. The cells inside the modules are organized in:
• 23 series and 46 parallel for the external modules;
• 25 series and 46 parallel for the internal modules.
Figure 9. Tesla Model 3 unassembled battery pack.
Each of the modules is composed of cylindrical cells disposed in series and parallel.
As can be seen, the two modules on the outer edges of the pack are smaller than the other
two central ones. This is not only a geometric placement difference, but a change in the
number of cells. As a matter of fact, the external modules are composed of 1058 cells while
the internal ones have 1150 units. The cells inside the modules are organized in:
•23 series and 46 parallel for the external modules;
•25 series and 46 parallel for the internal modules.
The Tesla Model 3 uses the model of 21,700 of cylindrical cells, the main features of
which are listed in Table 3.
Table 3. Tesla Model 3 main battery cell parameters.
Parameter Value Unit
Cell height 70 mm
Cell diameter 21 mm
Cell mass 68.5 g
Nominal capacity 4.80 Ah
Maximum continuous current 7.0 A
Maximum peak current 17.8 A
Energy @C/10 17.1 Wh
Continuous power 24.0 W
Peak power 64.6 W
World Electr. Veh. J. 2023,14, 337 20 of 28
Regarding the Thévenin parameters, the PerfECT tool is designed to receive variable
parameters according to internal states of the battery, for example: R
0
, R
1
, C
1
, R
2
and C
2
can vary with SOC, temperature, charge/discharge direction, aging, etc. In the specific case
of the Tesla Model 3, not all parameters were used, and the model was only based on the
SOC (for the other dimensions the same parameter values were maintained, so no effective
variations were observed). Table 4shows the used values for each SOC level, as well as the
reference open-circuit voltage for that state of charge.
Table 4. Tesla Model 3 Thévenin parameters varying with SOC.
SOC VOC [V] R0 [Ω] R1 [Ω] C1 [F] R2 [Ω] C2 [F]
0.00 2.75 0.030 0.0064 200 0.0064 1000
0.10 2.96 0.028 0.0064 250 0.0064 2500
0.20 3.17 0.026 0.0072 750 0.0064 8500
0.30 3.33 0.027 0.0072 1100 0.0064 12,000
0.40 3.53 0.025 0.0072 1450 0.0064 10,000
0.50 3.72 0.023 0.008 1650 0.008 15,000
0.60 3.88 0.024 0.0088 1800 0.0096 21,500
0.70 3.96 0.026 0.0088 2000 0.008 15,000
0.80 4.08 0.027 0.0128 2250 0.0096 15,000
0.90 4.18 0.029 0.024 2100 0.016 22,500
1.00 4.20 0.030 0.0216 2250 0.02 30,000
The chosen Tesla Model 3 presents an interesting powertrain layout—two electric
motors, front and rear, with different EM architectures—which makes the analysis more
complex but allows for the study of some thought-provoking control choices and vehicle
responses. The EM parameters can be found in Table 5.
Table 5. Tesla Model 3 front and rear EM main parameters.
Parameter Value Unit
Front motor (Induction Motor)
Pole pairs 2 -
Max continuous current 532 A
Max peak current 940 A
Max continuous torque 172 N ×m
Max peak torque 220 N ×m
Max continuous power 89.77 kW
Max peak power 158.0 kW
Max rotational speed 18,000 rpm
Rotational inertia 0.1 kg ×m2
Transmission ratio 9:1 -
World Electr. Veh. J. 2023,14, 337 21 of 28
Table 5. Cont.
Parameter Value Unit
Rear motor (Synchronous Motor)
Pole pairs 3 -
Max continuous current 600 A
Max peak current 1000 A
Max continuous torque 315 N ×m
Max peak torque 430 N ×m
Max continuous power 110.0 kW
Max peak power 192.0 kW
Max rotational speed 18,000 rpm
Rotational inertia 0.1 kg ×mm2
Transmission ratio 9:1 -
4.2. Experimental Methodology
When starting the analysis of the experimental setup, it is important to define the track
used during the campaign. The chose venue was the MotorOasi in the city of Susa, near
Torino in northern Italy (Figure 10). These facilities are used both for vehicle testing and for
driving courses, and have a series of different features, such as a low-adherence road and
external disturbances with floor actuators.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 10 of 14
Figure 10. Tesla Model 3 during the experimental campaign.
Environmental conditions were mild and constant, with temperatures between 23
and 28 °C, air humidity between 61 and 74% and wind speeds not exceeding 11 km/h.
Three main maneuvers were performed during the campaign: 0-100-0 accelerations,
a double-lane change [77] (as per the ISO 3888-2 standard [78]), and constant-radius cor-
nering.
The Tesla Model 3 was also chosen as the key vehicle to be analyzed because of the
availability of the CAN Bus data through its DBC file, making it possible to access a myr-
iad of internal signals present in the vehicle. Some of the most relevant signals include:
Body accelerations in the three directions;
Vehicle speed;
Pitch and roll angles and velocities;
Yaw rate;
Steering wheel angle and speed;
Wheel rotational speed (FL, FR, RL, RR);
Bus high voltage (front and rear);
Bus current (front and rear);
Acceleration pedal position;
Brake pedal activation signal (ON/OFF);
ABS activation flag;
ESP activation flag and related parameters;
Motor torque request (front and rear);
Motor output torque (front and rear);
Motor output power (front and rear);
Envelope of motor phase current (front and rear);
Battery state of charge;
Battery voltage;
GPS positioning (latitude and longitude).
Apart from the listed signals, a series of other channels are accessible, describing sev-
eral internal parameters of the BMS, user interface information, recharging status,
ADAS/autopilot, HVAC, etc. Overall, more than 3000 different signals can be extracted
from the CAN Bus reading.
Nevertheless, some signals and sensors are not present, not even in the most modern
and connected vehicles such as the Tesla Model3, and this motivated further instrumen-
tation of the track tests. The vehicle’s layout with the added sensors is shown in Figure 11.
Figure 10. Tesla Model 3 during the experimental campaign.
The main areas of the track used in the tests were the 300 m straight line, and the
middle rim of the roundabout, with a 75 m diameter and a width of 20 m.
Environmental conditions were mild and constant, with temperatures between 23 and
28 ◦C, air humidity between 61 and 74% and wind speeds not exceeding 11 km/h.
Three main maneuvers were performed during the campaign: 0-100-0 accelerations, a
double-lane change [
77
] (as per the ISO 3888-2 standard [
78
]), and constant-radius cornering.
The Tesla Model 3 was also chosen as the key vehicle to be analyzed because of the
availability of the CAN Bus data through its DBC file, making it possible to access a myriad
of internal signals present in the vehicle. Some of the most relevant signals include:
World Electr. Veh. J. 2023,14, 337 22 of 28
•Body accelerations in the three directions;
•Vehicle speed;
•Pitch and roll angles and velocities;
•Yaw rate;
•Steering wheel angle and speed;
•Wheel rotational speed (FL, FR, RL, RR);
•Bus high voltage (front and rear);
•Bus current (front and rear);
•Acceleration pedal position;
•Brake pedal activation signal (ON/OFF);
•ABS activation flag;
•ESP activation flag and related parameters;
•Motor torque request (front and rear);
•Motor output torque (front and rear);
•Motor output power (front and rear);
•Envelope of motor phase current (front and rear);
•Battery state of charge;
•Battery voltage;
•GPS positioning (latitude and longitude).
Apart from the listed signals, a series of other channels are accessible, describing
several internal parameters of the BMS, user interface information, recharging status,
ADAS/autopilot, HVAC, etc. Overall, more than 3000 different signals can be extracted
from the CAN Bus reading.
Nevertheless, some signals and sensors are not present, not even in the most modern
and connected vehicles such as the Tesla Model3, and this motivated further instrumenta-
tion of the track tests. The vehicle’s layout with the added sensors is shown in Figure 11.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 11 of 14
Figure 11. Tesla Model 3 sensors and datalogging layout.
Some of the sensors were installed in the vehicle for other experimental goals, such
as the brake pedal load cell (used to correlate the driver braking effort with the system
response) or the strain-gauged bolts, serving to test the procedure of wheel load estima-
tion, as described in [79].
After the acquisition and logging, an important step in the analysis is the post-pro-
cessing of the signals. The process, conducted in MATLAB 2023a, followed these steps
[79]:
Validation—verification of each signal to guarantee the coherence and magnitude
regarding the physical value anticipated;
Data cleanse—cancelling of missing data points, zero values and other eventual out-
liers or faulty signals;
Integration—gathering data from the different dataloggers, ensuring the synchroni-
zation of the information;
Determination of the relevant maneuvers—the acquisition begins before the actual
start of the maneuver, necessitating a “cut” of the data where useful information is
lacking;
Filtering—in signals with high noise, low-pass filters are applied to smooth the curve
and help with the data analysis and comparison.
5. Experimental Results
In this session, an extract of the main experimental results is presented, highlighting
the main parameters that demonstrate the precision of the proposed methodology. More
specifically, two maneuvers are presented: the straight line 0-100-0 event, with which it is
possible to validate the overall longitudinal dynamics and e-powertrain electro-mechani-
cal response; and the double-lane change, especially useful for the validation of lateral
dynamics and handling.
5.1. Straight Line 0-100-0 km/h
In Figure 12, it is possible to see four of the main parameters related to the longitudi-
nal dynamics and the electro-mechanical response related to the e-powertrain.
Figure 11. Tesla Model 3 sensors and datalogging layout.
Some of the sensors were installed in the vehicle for other experimental goals, such
as the brake pedal load cell (used to correlate the driver braking effort with the system
response) or the strain-gauged bolts, serving to test the procedure of wheel load estimation,
as described in [79].
After the acquisition and logging, an important step in the analysis is the post-
processing of the signals. The process, conducted in MATLAB 2023a, followed these
steps [79]:
World Electr. Veh. J. 2023,14, 337 23 of 28
•Validation
—verification of each signal to guarantee the coherence and magnitude
regarding the physical value anticipated;
•Data cleanse
—cancelling of missing data points, zero values and other eventual
outliers or faulty signals;
•Integration
—gathering data from the different dataloggers, ensuring the synchroniza-
tion of the information;
•Determination of the relevant maneuvers
—the acquisition begins before the actual
start of the maneuver, necessitating a “cut” of the data where useful information is
lacking;
•Filtering
—in signals with high noise, low-pass filters are applied to smooth the curve
and help with the data analysis and comparison.
5. Experimental Results
In this session, an extract of the main experimental results is presented, highlighting
the main parameters that demonstrate the precision of the proposed methodology. More
specifically, two maneuvers are presented: the straight line 0-100-0 event, with which it is
possible to validate the overall longitudinal dynamics and e-powertrain electro-mechanical
response; and the double-lane change, especially useful for the validation of lateral dynam-
ics and handling.
5.1. Straight Line 0-100-0 km/h
In Figure 12, it is possible to see four of the main parameters related to the longitudinal
dynamics and the electro-mechanical response related to the e-powertrain.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 12 of 14
(a) (b)
(c) (d)
Figure 12. Comparison between experimental and simulation data on the 0-100-0 km/h maneuver:
(a) vehicle speed; (b) electric motor torque; (c) DC current at bus; and (d) bus voltage.
The experimental and simulated trends are well correlated. Both in terms of shape
and magnitude, all four simulated parameters follow the observed curves obtained on the
track tests.
The main difference found in the comparison of the plots in Figure 12 lies on the
braking phase, from the time of 6.1 s. Indeed, the logic ruling the torque split between the
front and rear motors during the regenerative braking phase was not directly tuned to
reflect the behavior of the Tesla Model 3, although this operation could be performed by
adjusting the “Energy Management System” shown in Figure 7.
Overall, it is possible to assert that the longitudinal response of the PerfECT design
tool is sufficiently accurate in its description of the vehicle’s behavior and can be effec-
tively used as a predictive tool during the design of BEVs.
5.2. Double-Lane Change at 50 km/h
A similar analysis can be performed by looking at the DLC manoeuvre, in this case
performed at a speed of 70 km/h. Four important features of the lateral dynamics are dis-
played in Figure 13.
Figure 12.
Comparison between experimental and simulation data on the 0-100-0 km/h maneuver:
(a) vehicle speed; (b) electric motor torque; (c) DC current at bus; and (d) bus voltage.
The experimental and simulated trends are well correlated. Both in terms of shape
and magnitude, all four simulated parameters follow the observed curves obtained on the
track tests.
The main difference found in the comparison of the plots in Figure 12 lies on the
braking phase, from the time of 6.1 s. Indeed, the logic ruling the torque split between
the front and rear motors during the regenerative braking phase was not directly tuned to
World Electr. Veh. J. 2023,14, 337 24 of 28
reflect the behavior of the Tesla Model 3, although this operation could be performed by
adjusting the “Energy Management System” shown in Figure 7.
Overall, it is possible to assert that the longitudinal response of the PerfECT design
tool is sufficiently accurate in its description of the vehicle’s behavior and can be effectively
used as a predictive tool during the design of BEVs.
5.2. Double-Lane Change at 50 km/h
A similar analysis can be performed by looking at the DLC manoeuvre, in this case
performed at a speed of 70 km/h. Four important features of the lateral dynamics are
displayed in Figure 13.
World Electr. Veh. J. 2023, 14, x FOR PEER REVIEW 13 of 14
(a) (b)
(c) (d)
Figure 13. Comparison between experimental and simulation data on the double-lane-change ma-
neuver: (a) lateral acceleration; (b) yaw rate; (c) side slip angle; and (d) roll angle.
For the virtual reproduction of the DLC maneuver, the steering angle observed in the
experimental tests is hard-inputted on the virtual driver to avoid differences caused by
the approach used by the human driver and the virtual driver (as is often the case). Also,
in this case it is easy to notice that the proposed model closely reflects the behavior seen
in the experimental tests. Apart from some residual noise coming from the experimental
equipment and a slight deviation between 2.5 and 3 s of the maneuver, the overall shape
of the curves and magnitude of the parameters proves to be accurate.
6. Conclusions
This article proposed a multi-step methodology for the modeling and simulation of
BEVs, entitled the PerfECT Design Tool. As the name suggests, this virtual simulation
method aims to provide a suitable strategy to support the early stages of the engineering
design process for electric vehicles.
The article described the theoretical background and main equations used to simu-
late the mechanical, electrical, and thermal behavior of an EV. From this theoretical back-
ground, it was possible to build a complete model combining MATLAB/Simulink and the
vehicle dynamics software VI-CRT, divided into four independent but sequential steps:
Performance, Energy, Currents, and Temperature.
This model was then validated through a series of experimental maneuvers per-
formed with a Tesla Model 3, demonstrating its accuracy. The PerfECT design tool can be
used, as proposed, to help during the first stages of the new EV design and represents a
contribution to the industry and academia as a comprehensive and increasingly complex
solution for simulations.
Funding: This research received no external funding.
Data Availability Statement: Data are contained within the article.
Acknowledgments: The content of this article was developed in the context of the author’s indus-
trial PhD program and partnership between Politecnico di Torino, CNR and Beond. Special thanks
Figure 13.
Comparison between experimental and simulation data on the double-lane-change
maneuver: (a) lateral acceleration; (b) yaw rate; (c) side slip angle; and (d) roll angle.
For the virtual reproduction of the DLC maneuver, the steering angle observed in the
experimental tests is hard-inputted on the virtual driver to avoid differences caused by
the approach used by the human driver and the virtual driver (as is often the case). Also,
in this case it is easy to notice that the proposed model closely reflects the behavior seen
in the experimental tests. Apart from some residual noise coming from the experimental
equipment and a slight deviation between 2.5 and 3 s of the maneuver, the overall shape of
the curves and magnitude of the parameters proves to be accurate.
6. Conclusions
This article proposed a multi-step methodology for the modeling and simulation of
BEVs, entitled the PerfECT Design Tool. As the name suggests, this virtual simulation
method aims to provide a suitable strategy to support the early stages of the engineering
design process for electric vehicles.
The article described the theoretical background and main equations used to simulate
the mechanical, electrical, and thermal behavior of an EV. From this theoretical background,
it was possible to build a complete model combining MATLAB/Simulink and the vehicle
dynamics software VI-CRT, divided into four independent but sequential steps: Perfor-
mance, Energy, Currents, and Temperature.
World Electr. Veh. J. 2023,14, 337 25 of 28
This model was then validated through a series of experimental maneuvers performed
with a Tesla Model 3, demonstrating its accuracy. The PerfECT design tool can be used, as
proposed, to help during the first stages of the new EV design and represents a contribution
to the industry and academia as a comprehensive and increasingly complex solution
for simulations.
Funding: This research received no external funding.
Data Availability Statement: Data are contained within the article.
Acknowledgments:
The content of this article was developed in the context of the author’s industrial
Ph.D. program and partnership between Politecnico di Torino, CNR and Beond. Special thanks
to Massimiliana Carello, Elisabetta Punta and all the team at Beond for their support during the
technical and experimental activities; acknowledgements also to the VI-Grade team for the software
license and technical support.
Conflicts of Interest: The author declares no conflict of interest.
References
1.
Automobile—Early Electric Automobiles|Britannica. March 2023. Available online: https://www.britannica.com/technology/
automobile/Early-electric-automobiles (accessed on 29 November 2023).
2.
What Was the Henney Kilowatt? 2018. Available online: https://blog.consumerguide.com/what-was-the-henney-kilowatt/
(accessed on 29 November 2023).
3.
Shahan, Z. Electric Car History (In Depth). 2015. Available online: https://cleantechnica.com/2015/04/26/electric-car-history/
(accessed on 29 November 2023).
4.
Zero-Emission Vehicle Program|California Air Resources Board. March 2023. Available online: https://ww2.arb.ca.gov/our-w
ork/programs/zero-emission-vehicle-program/about (accessed on 29 November 2023).
5. Berdichevsky, G.; Kelty, K.; Straubel, J.; Toomre, E. The Tesla Roadster Battery System; Tesla Motors: Austin, TX, USA, 2006.
6. Blomgren, G.E. The Development and Future of Lithium Ion Batteries. J. Electrochem. Soc. 2016,164, A5019. [CrossRef]
7.
EEC. Council Directive 91/441/EEC of 26 June 1991 amending Directive 70/220/EEC on the approximation of the laws of the
Member States relating to measures to be taken against air pollution by emissions from motor vehicles. Off. J. L
1991
,242, 1–106.
8.
Q&A: Commission Proposal on the New Euro 7 Standards, Text. March 2023. Available online: https://ec.europa.eu/commissio
n/presscorner/detail/en/qanda_22_6496 (accessed on 29 November 2023).
9.
Fit for 55: Zero CO
2
Emissions for New Cars and Vans in 2035|News|European Parliament. 2023. Available online: https://www.
europarl.europa.eu/news/en/press-room/20230210IPR74715/fit-for-55-zero-co2-emissions-for-new-cars-and-vans-in-2035
(accessed on 29 November 2023).
10.
Deal Confirms Zero-Emissions Target for New Cars and Vans in 2035|News|European Parliament. 2022. Available online:
https://www.europarl.europa.eu/news/en/press-room/20221024IPR45734/deal-confirms-zero-emissions-target-for-new-cars-
and-vans-in-2035 (accessed on 29 November 2023).
11.
Frith, J.T.; Lacey, M.J.; Ulissi, U. A non-academic perspective on the future of lithium-based batteries. Nat. Commun.
2023
,14, 420.
[CrossRef]
12.
Electric Vehicles—Worldwide|Statista Market Forecast. March 2023. Available online: https://www.statista.com/outlook/mmo
/electric-vehicles/worldwide (accessed on 29 November 2023).
13.
Electric Vehicle Market Share, Size, Analysis|EV Market Growth. March 2023. Available online: https://www.alliedmarketresear
ch.com/electric-vehicle-market (accessed on 29 November 2023).
14.
Battery Recycling Policies for Boosting Electric Vehicle Adoption: Evidence from a Choice Experimental Survey. March 2023.
Available online: https://www.springerprofessional.de/en/battery-recycling-policies-for-boosting-electric-vehicle-adoptio/
23137392 (accessed on 29 November 2023).
15.
Nong, G.P.; Pang, S.L. Research on the Electric Vehicle Remanufacturable Battery Supply Chain with Recycling Channels. Adv.
Mater. Res. 2013,773, 948–953. [CrossRef]
16.
Feng, S. System dynamics model for battery recycling of electric vehicles in Anylogic simulation. Int. J. Internet Manuf. Serv.
2018
,
5, 405–418. [CrossRef]
17.
Hao, F.; Lu, X.; Qiao, Y.; Chen, X. Crashworthiness Analysis of Electric Vehicle with Energy-Absorbing Battery Modules. J. Eng.
Mater. Technol. 2017,139, 021022. [CrossRef]
18.
Kang, S.; Kwon, M.; Yoon Choi, J.; Choi, S. Full-scale fire testing of battery electric vehicles. Appl. Energy
2023
,332, 120497.
[CrossRef]
19.
Kim, S.; Lee, J.; Lee, C. Does Driving Range of Electric Vehicles Influence Electric Vehicle Adoption? Sustainability
2017
,9, 1783.
[CrossRef]
20.
Kumar, L.; Ravi, N. Electric vehicle charging method and impact of charging and discharging on distribution system: A review.
Int. J. Electr. Hybrid Veh. 2022,14, 87–111. [CrossRef]
World Electr. Veh. J. 2023,14, 337 26 of 28
21.
Dong, J.; Lin, Z. Within-day recharge of plug-in hybrid electric vehicles: Energy impact of public charging infrastructure. Transp.
Res. Part Transp. Environ. 2012,17, 405–412. [CrossRef]
22.
Gruber, P.W.; Medina, P.A.; Keoleian, G.A.; Kesler, S.E.; Everson, M.P.; Wallington, T.J. Global Lithium Availability. J. Ind. Ecol.
2011,15, 760–775. [CrossRef]
23.
Ahmed, S.; Nelson, P.A.; Gallagher, K.G.; Susarla, N.; Dees, D.W. Cost and energy demand of producing nickel manganese cobalt
cathode material for lithium ion batteries. J. Power Sources 2017,342, 733–740. [CrossRef]
24.
Rieck, F.; Machielse, K.; van Duin, R. Will Automotive Be the Future of Mobility? Striving for Six Zeros. World Electr. Veh. J.
2020
,
11, 10. [CrossRef]
25.
Girardi, P.; Gargiulo, A.; Brambilla, P.C. A comparative LCA of an electric vehicle and an internal combustion engine vehicle
using the appropriate power mix: The Italian case study. Int. J. Life Cycle Assess. 2015,20, 1127–1142. [CrossRef]
26.
Eshetu, G.G.; Zhang, H.; Judez, X.; Adenusi, H.; Armand, M.; Passerini, S.; Figgemeier, E. Production of high-energy Li-ion
batteries comprising silicon-containing anodes and insertion-type cathodes. Nat. Commun. 2021,12, 5459. [CrossRef]
27.
Varzi, A.; Raccichini, R.; Passerini, S.; Scrosati, B. Challenges and prospects of the role of solid electrolytes in the revitalization of
lithium metal batteries. J. Mater. Chem. A 2016,4, 17251–17259. [CrossRef]
28.
Braga, M.H.; Grundish, N.S.; Murchison, A.J.; Goodenough, J.B. Alternative strategy for a safe rechargeable battery. Energy
Environ. Sci. 2017,10, 331–336. [CrossRef]
29.
Rizzello, A.; Scavuzzo, S.; Ferraris, A.; Airale, A.G.; Carello, M. Temperature-Dependent Thévenin Model of a Li-Ion Battery for
Automotive Management and Control. In Proceedings of the 2020 IEEE International Conference on Environment and Electrical
Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Madrid, Spain, 9–12 June
2020; IEEE: Madrid, Spain, 2020; pp. 1–6, ISBN 978-1-72817-455-6. [CrossRef]
30.
Rizzello, A.; Scavuzzo, S.; Ferraris, A.; Airale, A.G.; Bianco, E.; Carello, M. Non-linear Kalman Filters for Battery State of Charge
Estimation and Control. In Proceedings of the 2021 International Conference on Electrical, Computer, Communications and
Mechatronics Engineering (ICECCME), Piscataway, NJ, USA, 7–8 October 2021; pp. 1–7. [CrossRef]
31.
Christensen, J.; Albertus, P.; Sanchez-Carrera, R.S.; Lohmann, T.; Kozinsky, B.; Liedtke, R.; Ahmed, J.; Kojic, A. A Critical Review
of Li/Air Batteries. J. Electrochem. Soc. 2011,159, R1–R30. [CrossRef]
32.
Wang, H.; Yang, Y.; Liang, Y.; Robinson, J.T.; Li, Y.; Jackson, A.; Cui, Y.; Dai, H. Graphene-Wrapped Sulfur Particles as a
Rechargeable Lithium–Sulfur Battery Cathode Material with High Capacity and Cycling Stability. Nano Lett.
2011
,11, 2644–2647.
[CrossRef]
33.
Ji, X.; Lee, K.T.; Nazar, L.F. A highly ordered nanostructured carbon–sulphur cathode for lithium–sulphur batteries. Nat. Mater.
2009,8, 500–506. [CrossRef]
34.
Hartmann, P.; Bender, C.L.; Sann, J.; Dürr, A.K.; Jansen, M.; Janek, J.; Adelhelm, P. A comprehensive study on the cell chemistry of
the sodium superoxide (NaO2) battery. Phys. Chem. Chem. Phys. 2013,15, 11661–11672. [CrossRef]
35.
Hartmann, P.; Bender, C.L.; Vraˇcar, M.; Dürr, A.K.; Garsuch, A.; Janek, J.; Adelhelm, P. A rechargeable room-temperature sodium
superoxide (NaO2) battery. Nat. Mater. 2013,12, 228–232. [CrossRef] [PubMed]
36.
All-Solid-State Lithium-Ion Batteries. March 2023. Available online: https://www.hitachizosen.co.jp/english/business/field/f
unctional/as-lib.html (accessed on 29 November 2023).
37.
Duan, Y.; Bai, X.; Yu, T.; Rong, Y.; Wu, Y.; Wang, X.; Yang, J.; Wang, J. Research progress and prospect in typical sulfide solid-state
electrolytes. J. Energy Storage 2022,55, 105382. [CrossRef]
38.
Suzuki, N.; Watanabe, T.; Fujiki, S.; Aihara, Y. Solid-State Batteries with Inorganic Electrolytes. In Encyclopedia of Electrochemistry;
John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2020; pp. 1–62. ISBN 978-3-527-61042-6. [CrossRef]
39.
Carello, M.; Pinheiro, H.D.C.; Longega, L.; Di Napoli, L. Design and Modelling of the Powertrain of a Hybrid Fuel Cell Electric
Vehicle. SAE Int. J. Adv. Curr. Pract. Mobil. 2021,3, 2878–2892. [CrossRef]
40.
Bianco, E.; Di Napoli, L.; Grano, E.; Carello, M. E-scooter Modelling: Battery and Fuel Cell System Integration. In Advances in
Italian Mechanism Science; Niola, V., Gasparetto, A., Quaglia, G., Carbone, G., Eds.; Springer International Publishing: Cham,
Switzerland, 2022; pp. 909–916. ISBN 978-3-031-10776-4. [CrossRef]
41.
Bianco, E.; Carello, M. A first e-scooter powertrain analysis for Fuel Cell integration. In Proceedings of the 2022 Interna-
tional Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), Maldives, Maldives,
16–18 November 2022; pp. 1–6. [CrossRef]
42.
Messana, A.; Airale, A.G.; Ferraris, A.; Sisca, L.; Carello, M. Correlation between thermo-mechanical properties and chemical
composition of aged thermoplastic and thermosetting fiber reinforced plastic materials: Korrelation zwischen thermomechanis-
chen Eigenschaften und chemischer Zusammensetzung von gealterten thermo- und duroplastischen faserverstärkten Kunst.
Mater. Werkst. 2017,48, 447–455. [CrossRef]
43.
Messana, A.; Sisca, L.; Ferraris, A.; Airale, A.G.; Pinheiro, H.d.C.; Sanfilippo, P.; Carello, M. From Design to Manufacture of a
Carbon Fiber Monocoque for a Three-Wheeler Vehicle Prototype. Materials 2019,12, 332. [CrossRef]
44.
Airale, A.; Carello, M.; Ferraris, A.; Sisca, L. Moisture effect on mechanical properties of polymeric composite materials. AIP Conf.
Proc. 2016,1736, 020020. [CrossRef]
45.
Carello, M.; Airale, A.G.; Ferraris, A.; Messana, A.; Sisca, L. Static Design and Finite Element Analysis of Innovative CFRP
Transverse Leaf Spring. Appl. Compos. Mater. 2017,24, 1493–1508. [CrossRef]
World Electr. Veh. J. 2023,14, 337 27 of 28
46.
Sisca, L.; Locatelli Quacchia, P.T.; Messana, A.; Airale, A.G.; Ferraris, A.; Carello, M.; Monti, M.; Palenzona, M.; Romeo, A.;
Liebold, C.; et al. Validation of a Simulation Methodology for Thermoplastic and Thermosetting Composite Materials Considering
the Effect of Forming Process on the Structural Performance. Polymers 2020,12, 2801. [CrossRef]
47.
Carello, M.; Pinheiro, H.d.C.; Messana, A.; Freedman, A.; Ferraris, A.; Airale, A.G. Composite Control Arm Design: A Compre-
hensive Workflow. SAE Int. J. Adv. Curr. Pract. Mobil. 2021,3, 2355–2369. [CrossRef]
48.
Fasana, A.; Ferraris, A.; Airale, A.G.; Berti Polato, D.; Carello, M. Experimental Characterization of Damped CFRP Materials with
an Application to a Lightweight Car Door. Shock Vib. 2017,2017, 7129058. [CrossRef]
49.
Carello, M.; Airale, A.G. Composite Suspension Arm Optimization for the City Vehicle XAM 2.0. In Design and Computation
of Modern Engineering Materials; Öchsner, A., Altenbach, H., Eds.; Springer International Publishing: Cham, Switzerland, 2014;
pp. 257–272. ISBN 978-3-319-07382-8. [CrossRef]
50.
Cubito, C.; Rolando, L.; Ferraris, A.; Carello, M.; Millo, F. Design of the Control Strategy for a Range Extended Hybrid Vehicle by
means of Dynamic Programming Optimization. In Proceedings of the 2017 IEEE Intelligent Vehicles Symposium (IV), Los Angeles,
USA, 11–14 June 2017; pp. 1234–1241. [CrossRef]
51.
Ferraris, A.; De Cupis, D.; De Carvalho Pinheiro, H.; Messana, A.; Sisca, L.; Airale, A.G.; Carello, M. Integrated Design and
Control of Active Aerodynamic Features for High Performance Electric Vehicles; SAE Technical Paper 2020-36-0079; SAE International:
Warrendale, PA, USA, 2021. [CrossRef]
52.
Brusaglino, G.; Buja, G.; Carello, M.; Carlucci, A.P.; Onder, C.H.; Razzetti, M. New technologies demonstrated at Formula Electric
and Hybrid Italy 2008. World Electr. Veh. J. 2009,3, 160–171. [CrossRef]
53.
Liu, B.; Zhang, H.; Zhu, S. An Incremental V-Model Process for Automotive Development. In Proceedings of the 2016 23rd
Asia-Pacific Software Engineering Conference (APSEC), Hamilton, New Zealand, 6–9 December 2016; pp. 225–232. [CrossRef]
54.
Castellanos Molina, L.M.; Manca, R.; Hegde, S.; Amati, N.; Tonoli, A. Predictive handling limits monitoring and agility
improvement with torque vectoring on a rear in-wheel drive electric vehicle. Veh. Syst. Dyn. 2023, 1–25. [CrossRef]
55.
Pinheiro, H.d.C.; Punta, E.; Carello, M.; Ferraris, A.; Airale, A.G. Torque Vectoring in Hybrid Vehicles with In-Wheel Electric
Motors: Comparing SMC and PID control. In Proceedings of the 2021 IEEE International Conference on Environment and
Electrical Engineering and 2021 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I CPS Europe), Bari, Italy,
7–10 September 2021; pp. 1–6. [CrossRef]
56.
Tramacere, E.; Castellanos, L.M.M.; Amati, N.; Tonoli, A.; Bonfitto, A. Adaptive LQR Control for a Rear-Wheel Steering
Battery Electric Vehicle. In Proceedings of the 2022 IEEE Vehicle Power and Propulsion Conference (VPPC), Merced, CA, USA,
1–4 November 2022; pp. 1–6. [CrossRef]
57.
De Carvalho Pinheiro, H.; Carello, M. Design and Validation of a High-Level Controller for Automotive Active Systems. SAE Int.
J. Veh. Dyn. Stab. NVH 2023,7, 83–98. [CrossRef]
58.
Vošahlík, D.; Haniš, T. Traction Control Allocation Employing Vehicle Motion Feedback Controller for Four-Wheel-Independent-
Drive Vehicle. IEEE Trans. Intell. Transp. Syst. 2023,24, 14570–14579. [CrossRef]
59.
Carello, M.; Ferraris, A.; Pinheiro, H.d.C.; Stanke, D.C.; Gabiati, G.; Camuffo, I.; Grillo, M. Human-Driving Highway Overtake
and Its Perceived Comfort: Correlational Study Using Data Fusion. In Proceedings of the WCX SAE World Congress Experience,
Detroit, MI, USA, 21–23 April 2020. SAE Technical Paper 2020-01-1036. [CrossRef]
60.
Pinheiro, H.d.C.; Stanke, D.C.; Ferraris, A.; Carello, M.; Gabiati, G.; Camuffo, I.; Grillo, M. Autonomous Driving Scenario
Generation in Overtake Manoeuvres Through Data Fusion. In Advances in Italian Mechanism Science; Niola, V., Gasparetto, A.,
Eds.; Springer: Berlin/Heidelberg, Germany, 2021; pp. 786–794. ISBN 978-3-030-55807-9. [CrossRef]
61.
Milliken, W.F. Race Car Vehicle Dynamics; Society of Automotive Engineers: Warrendale, PA, USA, 1995; ISBN 978-0-7680-0103-7.
62.
Pinheiro, H.d.C.; Carello, M.; Punta, E. Torque Vectoring Control Strategies Comparison for Hybrid Vehicles with Two Rear
Electric Motors. Appl. Sci. 2023,13, 8109. [CrossRef]
63.
Genta, G.; Morello, L. The Automotive Chassis; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2008; Volume 1–2,
ISBN 978-1-4020-8676-2.
64. VI-grade GmbH. VI-CarRealTime 20.0 Documentation; VI-grade GmbH: Darmstadt, Germany, 2020.
65.
Ydrefors, L.; Hjort, M.; Kharrazi, S.; Jerrelind, J.; Stensson Trigell, A. Rolling resistance and its relation to operating conditions: A
literature review. Proc. Inst. Mech. Eng. Part J. Automob. Eng. 2021,235, 2931–2948. [CrossRef]
66.
Nicoletti, L.; Mayer, S.; Brönner, M.; Schockenhoff, F.; Lienkamp, M. Design Parameters for the Early Development Phase of
Battery Electric Vehicles. World Electr. Veh. J. 2020,11, 47. [CrossRef]
67.
Electric Powertrain: Energy Systems, Power Electronics and Drives for Hybrid, Electric and Fuel Cell Vehicles | Wiley. April 2023.
Available online: https://www.wiley.com/en-au/Electric+Powertrain%253A+Energy+Systems%252C+Power+Electronics+a
nd+Drives+for+Hybrid%252C+Electric+and+Fuel+Cell+Vehicles-p-9781119063643 (accessed on 29 November 2023).
68. Krishnan, R. Electric Motor Drives: Modeling, Analysis, and Control; Pearson: London, UK, 2001; ISBN 978-0-13-091014-1.
69.
Bianco, E.; Rizzello, A.; Ferraris, A.; Carello, M. Modeling and experimental validation of vehicle’s electric powertrain. In
Proceedings of the 2022 IEEE International Conference on Environment and Electrical Engineering and 2022 IEEE Industrial and
Commercial Power Systems Europe (EEEIC /I&CPS Europe), Prague, Czech Republic, 28 June–1 July 2022; pp. 1–6. [CrossRef]
70.
Grano, E.; Bianco, E.; De Carvalho Pinheiro, H.; Carello, M. MTPA and flux weakening control of electric motors: A numerical
approach. In Proceedings of the 2023 IEEE International Conference on Environment and Electrical Engineering and 2023 IEEE
Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), Madrid, Spain, 6–9 June 2023; pp. 1–7. [CrossRef]
World Electr. Veh. J. 2023,14, 337 28 of 28
71.
Muhlethaler, J.; Biela, J.; Kolar, J.W.; Ecklebe, A. Core Losses Under the DC Bias Condition Based on Steinmetz Parameters. IEEE
Trans. Power Electron. 2012,27, 953–963. [CrossRef]
72.
Ciampolini, M.; Fazzini, L.; Berzi, L.; Ferrara, G.; Pugi, L. Simplified Approach for Developing Efficiency Maps of High-Speed
PMSM Machines for Use in EAT Systems Starting from Single-Point Data. In Proceedings of the 2020 IEEE International
Conference on Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe
(EEEIC/I&CPS Europe), Madrid, Spain, 9–12 June 2020; pp. 1–6. [CrossRef]
73.
Stevens, J. Fundamentals of Thermal Resistance, HeatSink blog by Celsia. 2018. Available online: https://celsiainc.com/heat-sin
k-blog/fundamentals-of-thermal-resistance/ (accessed on 29 November 2023).
74.
Wang, B.; Nie, Y.; Yang, Z.; Zong, C.; Geng, L. Study on the Barycenter Position of Measurement and Data Processing for Dura-Axle
Vehicle; Atlantis Press: Amsterdam, The Netherlands, 2016; ISBN 978-94-6252-188-9. [CrossRef]
75.
Zhao, X.; Kang, J.; Lei, T.; Wang, Y.; Cao, Z. Vehicle Centroid Measurement System Based On Forward Tilt Method Error Analysis.
IOP Conf. Ser. Mater. Sci. Eng. 2018,452, 042189. [CrossRef]
76.
Pinheiro, H.d.C.; Messana, A.; Carello, M.; Rosso, N. Multibody Parameter Estimation: A Comprehensive Case-Study for an
Innovative Rear Suspension. In Proceedings of the SAE BRASIL 2022 Congress, Sao Paulo, Brazil, 24–27 November 2022; SAE
Technical Paper 2022-36-0059. SAE International: Sao Paulo, Brazil, 2023. [CrossRef]
77.
Fehér, Á.; Aradi, S.; Bécsi, T. Hierarchical Evasive Path Planning Using Reinforcement Learning and Model Predictive Control.
IEEE Access 2020,8, 187470–187482. [CrossRef]
78.
BS ISO 3888-2:2011; Passenger Cars—Test Track for a Severe Lane-Change Manoeuvre. ISO International Standards: Geneva,
Switzerland, 2011.
79.
De Carvalho Pinheiro, H.; Sisca, L.; Carello, M.; Ferraris, A.; Airale, A.G.; Falossi, M.; Carlevaris, A. Methodology and Application on
Load Monitoring Using Strain-Gauged Bolts in Brake Calipers; SAE Technical Paper 2022-01-0922; SAE International: Warrendale, PA,
USA, 2022. [CrossRef]
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