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Abstract – In a few years, Tesla Motors Inc. has succeeded in
establishing itself as one of the market leaders in the electric car
market. The Tesla Model S, its first flagship vehicle, still arouses
the interest and curiosity of engineers around the world, thanks
to the manufacturer’s technological secrets and bold choices, in
particular about the unusual use of an induction machine in a
mass-produced car. Thus, this article aims to present an accurate
2D finite element model of the Tesla Model S 60 induction motor.
For this purpose, all the needed data are gathered and
completed. Then, a model of the machine is made with Altair
Flux2DTM software and several operating points are simulated in
order to validate the created model, according to data available
in literature. Finally, an analysis of the machine design or
operating conditions is made in order to propose possible
justifications to some of the technical choices made by Tesla
engineers.
Index Terms—2D finite element modeling, die-cast copper
rotor, reverse engineering, squirrel cage induction machine,
Tesla Model S
I. INTRODUCTION
ESLA, Inc. became in only a few years one of the main
electrical car manufacturer in the world. This success is,
at least in part, attributable to their numerous technical
innovations from the batteries to the electrical drive. In this
context, the American manufacturer made an unusual choice,
for its Model S, which is the 2015 and 2016 best-selling
electric car in the world [1], to use an induction motor. Indeed,
although induction machines have several advantages, like
their robustness, easier maintenance or lower price, they are
also less efficient with a lower power-to-weight ratio
compared to permanent magnet synchronous machines that
are more extensively used in the automotive sector [2], [3].
However, the Tesla Model S presents impressive
performances in terms of acceleration, output power or even
range, arousing engineers’ interest and curiosity about its
conception and design [4], [5]. Even though these
performances are due to the entire electrical drive system, the
paper only addresses the induction machine design.
Thus, the paper aims to gather and complete all the
available data on the Tesla Model S induction motor in order
to produce a synthesis that will be used to make a 2D finite
element model with Altair Flux2DTM software. Then,
simulation results are compared to theoretical performances
found in literature in order to validate the machine model.
Based on this model, an analysis of the motor design and
operation is finally proposed in order to put forward possible
justifications for the technical choices made by Tesla
engineers that are sometimes unusual.
II. TESLA MODEL S INDUCTION MOTOR DATA SYNTHESIS
All the necessary information are found in the literature.
Tesla patents are one of the main data sources, especially for
1Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, F-38000 Grenoble,
France
the stator and rotor geometry and windings. Several authors
have also studied or tested these data and even sometimes
completed them with measurements from the real motor [6]-
[8]. Moreover, general performances information given by
Tesla or available Model S dynamometer charts are used as
references in order to validate the modeling of Tesla Motors
induction machine.
A. General data
Thus, the machine used by Tesla for its “standard” Model
S 60 is a four poles squirrel cage induction motor [6]. The
studied version of the Model S can deliver up to 225 kW, with
a maximum torque of 430 Nm and a maximum speed of
15,000 rpm. It has 60 stator slots and 74 rotor bars, as it is
shown in figure 1. The squirrel cage is made of pure copper,
which provides several benefits that will be discussed later in
the paper. As no information could be found on the electrical
steel used by Tesla, M250-35A non-grain oriented electrical
steel sheets are used for the modeling [7], [8]. Indeed, thanks
to their high magnetic performances and thickness, it can be
quite confidently assumed that real electrical sheets would
present similar characteristics. The cooling system is made of
two different parts : the stator is cooled using a classical water
jacket and the heat is extracted from the rotor using a spiral
shaft groove [7], as it is shown in figure 2.
Fig. 1. Axial view of Tesla Model S induction motor [8]
Fig. 2. Machine cross-section with representation of the cooling system [6]
*Institute of Engineering Univ. Grenoble Alpes
Modeling and design analysis of the Tesla
Model S induction motor
R. Thomas1, L. Garbuio1, L. Gerbaud1, H. Chazal1
T
Cooling fluid
Cooling
jacket
Rotor
cooling
system
B. Main geometrical data
As it has been said previously, Tesla patents offer one of
the main sources of information especially concerning the
geometry dimensions, with several range of values or ratios
[9], [10]. Thus, some of the values are directly given and some
others are found using these ratios with different levels of
uncertainty. The main dimensions used for the model are
summarized in table 1 and can be seen in figure 3.
In order to select and validate all the model geometrical
dimensions, different possibilities are tested and the values
that enable to reach the desired performances are kept.
However, even though these values might not be the exact
dimensions of the real motor, they are still used as the main
goal here is to propose a model close enough to the reality to
be usable for other purposes, e.g. pedagogical, reverse-
engineering or optimization projects. The data with the
greatest uncertainty are indicated using italic in table 1.
TABLE I
TESLA MODEL S INDUCTION MOTOR MAIN DIMENSIONS
Parameter name Symbols
used
Values used in the
proposed model
Stack length
L
152 mm
Air gap
e
0.5 mm
Stator
Stator outer diameter
D
254 mm
Stator inner diameter
D
156.8 mm
Slot depth
L
19 mm
Slot opening width
W
2.9 mm
Tooth tip depth
L
1 mm
Tooth width
W
4.5 mm
Rotor
Rotor outer diameter
𝐷
155.8 mm
Rotor inner diameter
𝐷
50 mm
Slot depth
𝐿
19.6 mm
Slot bridge
𝐿
0.55 mm
Tooth width
𝑊
4.5 mm
Fig. 3. Axial view of stator slots and rotor bars with dimensions [8]
C. Main electrical data
The motor is directly fed by an inverter. The DC bus
voltage is 366 V, which means a maximum phase-to-neutral
rms voltage of 150 V. The maximum peak current for the
stator windings is 1,273 A, which means a maximum rms
current of approximately 900 A [7], [8].
The Tesla patent [11] depicts several possible windings.
These different configurations were studied in paper [8], but
only one winding pattern seems to be possible as it is the only
one enabling to reach the theoretical performances. Thus, this
configuration consists of a concentric set of three coils per
pole and per phase with a coil pitch of 10-12-14 and turns per
coil of 1-2-2 [7]. The conductors are composed of 26 stranded
round wires with a diameter of 1.08 mm and an individual
insulation of 0.074 mm [6]. Each phase is separated into two
paths that are connected in parallel. This enables to use a 3-
phase or 6-phase configuration, depending on the desired
control system, as it is presented in paper [7], but also for
safety reasons, to prevent a potential power supply failure or
the destruction of a stator winding. Moreover, it enables to
increase the resulting voltage across each coil.
In order to simulate the motor model, the equivalent
electrical diagram needs to be implemented. Thus, it is created
from the phase schematic provided by Tesla in its patents, as
it can be seen in figure 4. The stator winding resistance is
computed using the machine and conductor geometry and
considering that the motor working temperature is around
150°C [7]. The resistances and leakage inductances of the
stator winding end turns and the squirrel cage end rings are
also computed using geometrical parameters and analytical
methods [12]. Finally, these different components are
connected together to voltage or current sources depending on
the desired kind of simulations. The obtained values for these
components in the 6-phase configuration and the used
materials properties are presented in table 2. These six phases
are then connected together to form three phases, as it is
shown in figure 4. The data with the greatest uncertainty are
indicated using italic.
Fig. 4. Tesla Model S induction motor equivalent electrical diagram [8]
TABLE II
VALUES OF THE COMPONENTS OF THE EQUIVALENT ELECTRICAL DIAGR AM
OF THE TESLA MODEL S INDUCTION MOTOR AND CHARACTERISTICS OF THE
USED MATERIALS
Parameter name Symbols
used
Values used in the
proposed model
Materials
Copper resistivity
(150°C)
𝜌
°
2
.
6
.
10
Ω
m
Electrical steel sheet
thickness /
0
.
35
𝑚𝑚
Initial relative
permeability
𝜇
16,642
Mean evaluated
permeability
𝜇
5,114
Saturation magnetization
𝐽
2 T
Electrical diagram components (6-phase configuration)
Stator winding resistance
𝑅
3
.
32
𝑚
Ω
Winding end turns
resistance
𝑅
3
.
83
𝑚
Ω
Winding end turns
leakage inductance
L
0
.
71
μ
H
Squirrel cage resistance
(between two bars)
𝑅
0
.
27
𝜇𝛺
Squirrel cage leakage
inductance (between two
bars)
𝐿
5
𝑛𝐻
𝐿
𝑊
𝑊
𝐿
𝑊
𝐿
𝐿
III. 2D FINITE ELEMENT (FE) MODEL
A. Hypotheses
Once the necessary data are gathered and completed, the
next step is to carry out the modeling with Altair FluxTM
software, taking into account the following hypotheses:
- Parameterized simulations in order to study how the
motor performances (e.g. stator rms voltage or
current, input and output power, torque, efficiency,
power factor…) vary according to the slip;
- Simulations are running under magneto harmonic
conditions: sinusoidal steady state at a given
frequency. Thus, the machine is supplied by a
balanced three-phase sinusoidal power supply;
- Depending on the studied operating point, the motor
is fed by three current or voltage sources with a
specified frequency. Indeed, at low speed operating
points the current is imposed at its maximum value
to study this operating limitation. On the contrary, at
high speed operating points the voltage is imposed.
The several studied working points are reached by
changing the value of the (current, frequency) or
(voltage, frequency) couples within the operating
limitations;
- Stator and rotor Joule losses are considered in this
model as well as iron losses that are estimated thanks
to a Bertotti model using electrical steel sheet
characteristics.
However, these hypotheses can easily be modified or
adapted by the user of the presented model according to his
needs, if he is not satisfied with them.
B. Finite Element Model
The resulting induction machine model is shown in figure
5. The flux density levels and the field lines for the maximum
power operating point are also represented.
The FE model is coupled with the machine equivalent
electrical diagram as it is shown in figure 6. The stator
windings and the squirrel cage, which are also represented
with FE, are represented using field-circuit coupling elements
such as coil conductors (2) or a squirrel cage component (4).
This electrical diagram enables to define all the external
electrical elements that shall be considered, such as the power
sources or the impedances of the stator windings end turns.
Fig. 5. Studied machine 2D FE model with flux density levels and field lines
at maximum power operating point (the flux density scale is limited to 2.1T
and the saturated areas are shown in grey)
For each simulation carried out, the different losses, the
power output and the power factor are calculated and
compared to the values found in papers [7] and [8].
Some of the numerical characteristics of the FE model are
presented in table 3. Thanks to the symmetries, the model is
reduced to half a machine.
Fig. 6. Electrical diagram of the studied machine 2D FE model with (1)
current sources, (2) field-circuit coupling components, (3) stator end winding
impedances and (4) squirrel cage
TABLE III
MAIN NUMERICAL CHARACTERISTICS OF THE FE MODEL
Characteristics Values
Mesh
Nodes 99,992
Linear
elements 13,573
Surface
elements 49,927
Computation time
(for 36 different slip values) 45 min
PC, 8.00 Go RAM, Intel Core i7, 3.40 GHz, Windows 10
C. Operating points studied
Several (current, frequency) couples are tested in order to
study the main operating points that are described in the
literature, like the maximum power operating point [8]. The
aim is to find the (current, frequency) couple that enables to
reach the desired performances and then to compare it to the
theoretical one. For each simulation, the entire torque Γ vs
speed Ω characteristic is drawn as the results are obtained as
a function of the slip. Moreover, the curve Γ(Ω) describing the
operating limitations is calculated considering current, power
or voltage limitations [13]. Then, this operating limitations
curve is used as a reference for our model in order to check if
it can reach these limitations with the announced
performances and, thus, validate this modeling. Finally, an
efficiency and total Joule losses maps are drawn and
compared to the maps found in papers [7] and [8].
IV. SIMULATION RESULTS AND MODEL VALIDATION
A. Maximum output power operating point results
The operating point that is the most described in the
literature, e.g. in papers [7] and [8], is the maximum output
power one. Thus, it is the first one that is simulated in order
to compare the results with the theoretical outcomes. The
curve Γ(Ω) is plotted (see figure 7). The main resulting values
are presented in table 4 and compared to the values obtained
from the thesis [7].
As it can be seen, the simulation results are very similar to
the theoretical ones. The main difference is the value of the
stator rms current that is higher than expected. Indeed, in
order to reach an output power and torque of respectively 225
kW and 430 Nm, it has been necessary to impose an input rms
current of 950 A instead of 900 A. This could be explained by
the small differences between the model and the real motor
due to data uncertainty. This uncertainty concerns some
geometrical parameters like the rotor bridges size, the
characteristics of the electrical steel used that are not precisely
known or the calculated electrical components, as it has been
1 2 3
4
𝑅
𝑅
𝐿
𝑅
𝐿
presented earlier in the paper. The observed differences could
also be due to the magneto-harmonic conditions and the
different hypotheses that might not provide very accurate
results especially for an induction motor. A simulation in
transient magnetic conditions of the same model is also
carried out, with voltage sources, and the results are slightly
different. Indeed, with an imposed rms voltage of 97.45 V, a
frequency of 166.7 Hz and a rotational speed of 4,880 rpm
which corresponds to a slip of 2.45%, the resulting rms
current is 885 A with an average output torque of 435 Nm.
Furthermore, as it is shown in figure 5, the flux density
levels, considering only the fundamental, are between 0.2 T
and the saturation level of the electrical steel. At this operating
point, Tesla engineers announce in their patent [10] the
average and maximum values of the flux density at the middle
of the air gap and at the middle of the rotor bridges. These
values are compared to the simulated results in the table 5.
Fig. 7. Torque = f (Speed) characteristic at maximum output power operating
point, with stator rms current 𝐼 and frequency f
TABLE IV
MAIN SIMULATION RESULTS AT MAXIMUM OUTPUT POWER OPERATING
POINT AND COMPARISON WITH MAIN RESULTS FROM LITER ATURE [7], [8]
Parameter Simulation results
Results from
the literature
[7], [8]
Input
Frequency 166.7 Hz /
Stator rms current 950 A 900 A
Stator rms voltage 97.45 V /
Output
Output power 225 kW 225 kW
Torque 430 Nm 430 Nm
Slip 2.45 % /
Rotor joule losses 5.5 kW /
Stator joule losses 9.7 kW /
Iron losses 365 W /
Total losses 15.6 kW > 12 kW
Efficiency 93.4 % 93-94 %
Power factor 0.85 /
TABLE V
COMPARISON OF THE AVERAGE AND MAXIMUM VALUES OF THE FLUX
DENSITY AT THE MIDDLE OF THE AIR GAP AND AT THE MIDD LE OF THE
ROTOR BRIDGES BETWEEN THE SIMULATED MOTOR AND TESLA P ATENT [10]
AT MAXIMUM OUTPUT POWER OPERATING POINT
Area Simulation
results
Results from
the Tesla
patent [10]
Middle of the
air gap
Average 0.74 T 0.8 T
Maximum 1.78 T 1.6 T
Middle of the
rotor bridges
Average 1.5 T 1.8 T
Maximum 2.55 T 2.4 T
Thus, the maximum output power operating point results
are very close to the results presented in Tesla patents or found
by different authors [7], [8], [10].
B. Operating limitations
In order to check if the presented model can reach every
operating limits described in paper [13], several operating
points are tested and presented in figure 8 (points 1 to 4) with
the corresponding value of the (current, frequency) or the
(voltage, frequency) couples. Indeed, there are many
possibilities to reach one operating point with an induction
machine, depending on the frequency, the voltage or the
current and the slip. Thus, as the needed voltages in order to
reach a torque of 430 Nm at low frequency range were not
known, the simulations are run with an imposed stator rms
current. For example, operating points 1 or 2 could be reached
in another way, by imposing the stator rms voltage, so, the
resulting Γ(Ω) curve would be different even if these points
would be reached with the same output values, like it is the
case for the fourth tested point. However, for high rotating
speeds, the simulations are run with an imposed stator voltage,
because this time, the required current to reach the limiting
output power is not known. The theoretical voltage, current
and power limits are also drawn in figure 8.
Fig. 8. Studied operating points and theoretical or effective operating
limitations with stator rms current 𝐼 or stator rms voltage 𝑉
and
frequency f
Thus, the tested limits are effectively reached by the model
with performances similar to the ones described in the paper
[13]. Depending on the sources, a torque limitation due to the
voltage limitation is sometimes defined after 8,000 rpm [13]
and defined as a “theoretical voltage limit” in figure 8.
However, as it can also be seen in figure 8, based on the
simulations presented in the paper, this limitation does not
really seem to exist. Indeed, the simulation of the operating
point 4 is run with voltage sources assigned at a rms value of
150 V, which corresponds to the maximum stator rms voltage
of the real Tesla Model S motor. Once again, it is the output
power limit that imposes the maximum operating point at
14,000 rpm and not voltage or current limits. Moreover, this
limitation does not clearly appear on Tesla Model S
dynamometer charts that can be found online [14]. This
limitation could, nevertheless, artificially exist, as it is
important to always preserve the possibility to further increase
the voltage in order to maintain the desired dynamic
performances. This point will be detailed later in the paper.
1 2
3
4
C. Efficiency and total Joule losses maps
Finally, in order to fully study and validate the model, an
efficiency and total Joule losses maps are drawn. In order to
do this, about 180 (current, frequency) or (voltage, frequency)
couples are simulated, for 35 different slip values each time.
The resulting simulated operating points are placed in the
(rotating speed, torque) system of axes and the corresponding
efficiency value is compared with that of the neighboring
points. As there are many possibilities to reach one operating
point, depending on the voltage, current, frequency and slip,
the aim is to eliminate the simulated points that have a lower
efficiency for similar operating conditions and to keep only
the optimal ones to draw the efficiency map. The precision of
these maps may seem limited, as it would have been necessary
to carry out a higher number of FE simulations to cover
precisely the entire operating area. However, considering the
simulation time of the FE model, this method enables to draw
approximated maps that can be used to compare the efficiency
of the main operating areas with other efficiency and Joule
losses maps, that are presented in papers [7] and [8], with an
acceptable simulation time. The resulting efficiency and total
Joule losses maps are respectively shown in figures 9 and 10.
Fig. 9. Machine FE model efficiency map (considering only stator and rotor
Joule losses and iron losses)
Fig. 10. Machine FE model total Joule losses map
The comparison with papers [7] and [8] shows that the
global shape of the two maps and the main efficiency and total
Joule losses levels are corresponding. Thus, these maps could
be used to study an entire operating cycle of the motor.
D. Model limits
As it has been shown previously, this model seems to fit in
with a good accordance to the Tesla Model S induction motor
that is described in the literature. However, some differences
remain, for example for the maximum stator rms current
needed to reach the maximum torque. The values of these
different errors are shown in table 6. These differences may
be due to the numerous uncertainties about some geometrical
parameters, like the rotor bridge size, about the materials
used, like the electrical steel characteristics, or about some
electrical parameters, like the stator end winding and the
squirrel cage end ring impedances. These different values are
analytically computed or chosen after several tests for this
model and might not exactly correspond to the real values.
Moreover, for the flux density values, the model presented
here may lead to less accurate results as it is only a 2D model
with all the linked assumptions and as there are various
uncertainties about the electrical steel characteristics. On the
other hand, it may be possible that Tesla’s values are obtained
with slightly different operating conditions, leading to
different flux density results for the same output values.
However, as it has been said previously, the paper mainly
aims to present a model close enough to the real motor, with
similar performances in order to be used as an example for
educational purposes or to prospect technological solutions.
Further investigations will enable to reduce these errors by
refining the model with direct measures on a real motor.
TABLE VI
MAIN ERRORS BETWEEN SIMULATION RESULTS AND VALUES FOUND IN
LITERATURE [7], [10]
Errors Value
Error on stator maximum rms current
5
.
6
%
Mean error on maximum flux density
through the motor
8
.
8%
Mean error on average flux density
through the motor
12
%
V. TESLA TECHNICAL CHOICES ANALYSIS
A. Rotor material choices
As it has been presented before, Tesla made the uncommon
choice for its induction machine rotor to use a squirrel cage
made up of pure copper instead of aluminum. This choice may
look logical as copper has a lower resistivity than aluminum.
Thus, the rotor Joule losses are much lower and the induced
currents are higher, leading to a higher torque and lower rotor
temperature, which is one of the main operating limitations
for induction machines [15], [16]. Hence, copper rotor
induction machines have a higher efficiency than aluminum
rotor machines.
Fig. 11. Tesla Model S induction motor copper rotor picture [17]
However, this technical choice is not widespread among
manufacturers because the rotor manufacturing method is
more complicated and expensive compared to the aluminum
rotor one, as it is presented in papers [15] and [16]. Even if
copper die-casting is similar, a main difference is that copper
melts at 1,083°C while aluminum alloys only melt around
670°C. Therefore, the manufacturing process requires to work
at higher temperatures and pressures. Moreover, copper has
other drawbacks, such as its higher density, which means a
higher rotor mass, a greater inertia and a higher mechanical
stress on rotor sheets. Copper also oxidizes quickly when
getting in contact with air.
Thus, the Tesla Model S motor model presented in the
paper has been used to compare the motor performances when
the squirrel cage is made up of copper or aluminum. The
simulation results are given in table 7. The simulated
operating point is the same than previously. It can be seen that
the aluminum squirrel cage motor logically produces more
rotor Joule losses, which leads to a lower efficiency.
Moreover, as the resulting motor equivalent impedance is
higher, the needed stator line-to-neutral voltage is slightly
higher but the power factor approximately remains the same.
TABLE VII
MAIN SIMULATION RESULTS AT MAXIMUM OUTPUT POWER OPERATING
POINT WITH THE PRESENTED MODEL FOR COPPER AND ALUMINUM ROTOR
Parameter Copper rotor Aluminum rotor
Input
Frequency 166.7 Hz 166.7 Hz
Stator rms current 950 A 950 A
Stator rms voltage 97.45 V 97.72 V
Output
Output power 225 kW 225 kW
Torque 430 Nm 430 Nm
Slip 2.45 % 4%
Rotor joule losses 5.5 kW 9 kW
Stator joule losses 9.7 kW 9.7 kW
Iron losses 365 W 365 W
Total losses 15.6 kW 19 kW
Efficiency 93.4 % 91.9 %
Power factor 0.85 0.84
B. Geometrical dimension choices
1) Electromagnetic considerations
The studied machine is made of a high number of stator or
rotor slots. This presents the advantage of smoothing the air
gap flux density distribution, making it appear more
sinusoidal. Thus, the resulting electromotive force harmonics
are also reduced, leading to less torque ripple.
Rotor slots are closed by bridges that remain usually highly
saturated. These slot bridges enable to simplify rotor die-
casting by preventing melted copper to flow out and provide
higher mechanical strength [18]. Moreover, closed-slot rotor
has a higher leakage impedance, which helps to reduce
electromagnetic noises, vibrations, stator current harmonics
and torque ripples. However, it also damages the power
factor, the starting and maximum torques and the efficiency.
Rotor bars are deep which could also be seen as a drawback
because this design increases the leakage fluxes, as the
resulting leakage conductivity is larger than before [19]. Thus,
the efficiency could be changed and reduced. As the low-
starting-current high-starting-torque objective can be
obtained thanks to the inverter control law, by applying
adapted starting voltage and frequency, it does not seem
interesting to use a deep-slot rotor [20]. Moreover, depending
on the frequency and slip, the resulting rotor resistance and
leakage inductance vary, for example because of the skin
effect, and, therefore, the resulting model implemented in the
control law has to be adapted regularly.
2) Thermal considerations
Although this design may have several disadvantages,
based on the arguments outlined above, a thermal analysis of
the machine also reveals several advantages. Indeed,
temperature is one of the main operating limitations in an
induction machine and cooling is a key element. The
extraction of the heat produced at the stator is generally
carried out by simple methods, using for example a cooling
fluid through a cooling jacket, as it is the case for the Tesla
Model S induction motor and as it has been presented
previously in the paper [7]. However, the extraction of the
heat produced at the rotor is more complex since it concerns
rotating parts. Yet, rotor cooling is essential to push back
operating limits and reach the desired performances. Thus,
Tesla have found an innovative solution [21] by using a
cooling fluid that is flowing along the machine shaft through
a spiral groove in order to extract the produced heat. Since the
rotor bars are made up of copper, having a thermal
conductivity higher than the one of aluminum, the use of deep
bars could have the advantage of directing the produced heat
flow on the rotor center where Tesla rotor cooling system
enables to extract the heat, as it is shown in figure 12.
Fig. 12. Schematic of the assumed rotor heat transfers
This design would therefore have an interest other than
simply electromagnetic, especially since rotor cooling is one
of the main challenges in the design of induction machines.
C. Operating condition choices
The various carried out simulations have shown that the
main operating limitations of the powertrain are not directly
due to the motor. Indeed, the real operating limitations of an
induction motor are mainly related to thermal considerations,
laminations saturation or mechanical resistance. This gives
current, voltage or speed limitations, depending on the
cooling system efficiency and the materials performances, but
these limitations can still be pushed back during a short delay.
However, in most cases, powertrains operating limitations are
lower than the real motor limits. Indeed, they are coming from
battery (power or voltage limits) or power electronics (current
or voltage limits).
As it has been shown previously, the main operating
limitation is due to the maximum output power. In fact, this
limitation comes from the used battery technology and
represents the maximum power it can deliver at once [22].
Indeed, in more recent Model S versions, the battery
performances have been improved and, therefore, the
maximum output power of the powertrain is higher [23].
Concerning the voltage limitation, it has been shown that
the theoretical limitation that appears after 8000 rpm might
not really exist as the motor is still able to deliver a higher
torque at maximum input voltage. However, the powertrain
control system always needs to be able to quickly increase or
decrease the stator voltage in order to maintain its imposed
Heat flow
Cooling fluid
Rotor bars
dynamic performances, like response times. To do this it is
necessary to ensure that the system always keeps a voltage
reserve, using an artificial voltage limitation for example.
VI. CONCLUSION & FUTURE WORKS
To conclude, the main general, geometrical or electrical
data that could be gathered or calculated for the Tesla Model
S 60 induction motor have been presented. This information
has been used in order to build a 2D finite element model of
this induction machine with Altair Flux2DTM software. This
model is representative of the behavior of the real motor, with
similar performances, as it has been shown by comparing the
tested operating points simulation results to the values that
could be found in Tesla patents or in the literature. All these
simulations enabled to validate the model. Finally, it has been
shown that this model enables to carry out technological
studies, e.g. the impact of the material used for the squirrel
cage and the stator slots or rotor bars dimension choices. It
has also been shown that thermal aspects have a major impact
on the machine design.
In future works, this model can be completed and refined
by measuring the geometry and testing directly a Model S
motor. Moreover, it could be interesting to develop an
analytical model of this machine from locked-rotor and no-
load FEM simulations in order to make further investigations
with simplified and faster simulations, e.g. for optimized
sizing. It would also be interesting to develop a thermal model
linked to the presented one in order to study the evolution of
the temperature through the motor depending on the operating
point. It could enable to demonstrate that the thermal sizing is
as important as the electromagnetic one, especially for an
induction motor whose temperature is one of the main
operating limits. However, the actual model can still be used
for reverse-engineering and pedagogical purposes.
The model of the Tesla Model S 60 induction motor that is
presented in this paper is downloadable at:
https://g2elab.grenoble-inp.fr/fr/le-laboratoire/download-the-
new-2d-finite-element-model-of-the-tesla-model-s-60-
induction-motor
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VIII. BIOGRAPHIES
Robin Thomas graduated from Grenoble INP - ENSE3 engineering school,
Grenoble, France, with a specialization in electrical engineering in 2019. The
same year, he integrated the Grenoble Electrical Engineering laboratory
(G2Elab) as a Ph.D. student. His thesis is focusing on the optimal design of
the coupling between electrical machine and unconventional power
electronics system.
Lauric Garbuio received the M.S. degree from Ecole Normale Superieure
de Cachan, Paris, France in 2001 and the Ph.D. degree in electrical
engineering in 2006 from the Institut National Polytechnique de Toulouse,
France. He joined the Electrical Engineering and Ferroelectricity Laboratory
(LGEF) of INSA Lyon as Associate Professor from 2007 to 2010 where he
worked on self-powered harvesting systems with smart materials for
powering sensors or autonomous Health Monitoring Systems. Since 2010, he
joined the Grenoble Electrical Engineering Laboratory (G2ELab) as
Associate Professor. His current research interests include the modeling and
conception of new electrical systems.
Laurent Gerbaud received the Ph.D degree in electrical engineering from
Grenoble-INP, Grenoble, France, in 1993. He was successively a Researcher,
an Assistant Professor, and now a Professor at the Grenoble Electrical
Engineering laboratory (G2Elab) and Grenoble-INP–UGA–CNRS. His
researches deal with the simulation and design of electrical systems. His
research interests include electrical drives and power electronics applications.
Hervé Chazal received an engineering degree from the Ecole Nationale
Superieure d’Ingénieurs Electriciens (ENSIEG) and the Ph.D. degree in
electrical engineering in 2004 from the Joseph Fourier University of
Grenoble, France. He joined the Grenoble Electrical Engineering Laboratory
(G2Elab) as Associate Professor in 2005. His current research interests
include soft magnetic materials, magnetic behavior characterization and
modeling, but also electromagnetic devices design.
