energies

Article
Inductive Electrically Excited Synchronous Machine for
Electrical Vehicles—Design, Optimization and Measurement
Samuel Müller * , David Maier and Nejila Parspour

Institute of Electrical Energy Conversion, University of Stuttgart, 70569 Stuttgart, Germany

* Correspondence: samuel.mueller@iew.uni-stuttgart.de

Abstract: The demand for electric machines has been rising steadily for several years—mainly due to
the move away from the combustion engine. Synchronous motors with rare earth permanent magnets
are widely used due to their high power densities. These magnets are cost-intensive, cost-sensitive
and often environmentally harmful. In addition to dispensing with permanent magnets, electrically
excited synchronous machines offer the advantage of an adjustable excitation and, thus, a higher
efficiency in the partial load range in field weakening operation. Field weakening operation is
relevant for the application of vehicle traction drive. The challenge of this machine type is the need
for an electrical power transfer system, usually achieved with slip rings. Slip rings wear out, generate
dust and are limited in power density and maximum speed due to vibrations. This article addresses
an electrically excited synchronous machine with a wireless power transfer onto the rotor. From the
outset, the machine is designed with a wireless power transfer system for use in a medium-sized
electric vehicle. As an example, the requirements are derived from the BMW’s i3. The wireless power
transfer system is integrated into the hollow shaft of the rotor. Unused space is thus utilized. The
overall system is optimized for high efficiency, especially for partial load at medium speed, with
an operation point-depending optimization method. The results are compared with the reference
permanent magnet excited machine. A prototype of the machine is built and measured on the test
bench. The measured efficiency of the inductive electrically excited synchronous machine is up to 4%
higher than that of the reference machine of the Bayerische Motoren Werke AG (BMW) i3.

Citation: Müller, S.; Maier, D.;

Keywords: electrically excited synchronous machine; wound field synchronous machine; rotating
Parspour, N. Inductive Electrically
wireless power transfer; electrical vehicle
Excited Synchronous Machine for
Electrical Vehicles—Design,
Optimization and Measurement.
Energies 2023, 16, 1657. https://
doi.org/10.3390/en16041657 1. Introduction

Academic Editors: David Gerada,

The number of electric vehicles increased in recent years. Due to the restrictions on
Yuting Gao and Tianjie Zou
local emissions, all automotive manufacturers are expanding their portfolio of electric cars.
In [1], is estimated that in 2030 more than half of the registered new vehicles in the United
Received: 17 January 2023 States will be an Electrical Vehicle (EV). Ref. [2] gives a detailed analysis of the future of
Revised: 1 February 2023 global electromobility. It shows that 18 of the 20 largest original equipment manufacturers
Accepted: 3 February 2023 have committed to increasing their offer and sales of EVs, in some cases significantly up to
Published: 7 February 2023
100% of new cars.
Due to the high power density of the neodymium iron boron magnets, Permanent
Magnet Synchronous Machines (PMSMs) are often used as Electrical Machine (EM) for EVs.
Copyright: © 2023 by the authors.
Especially for hybrid vehicles, where the EM and the combustion engine are mounted on
Licensee MDPI, Basel, Switzerland.
the same axle, the power density is of great importance. The drawbacks of the magnets are
This article is an open access article
price sensitivity [3] (especially estimated for the growing market of electric powertrains),
distributed under the terms and availability and sustainability [4].
conditions of the Creative Commons The magnet volume could be decreased by increasing the reluctance torque, called
Attribution (CC BY) license (https:// Permanent Magnet-Assisted Synchronous Reluctance Motor (PMASRs), see [5,6]. Some
creativecommons.org/licenses/by/ investigations significantly reduce the permanent magnetic field to avoid rare earth magnets
4.0/). and use ferrite magnets. The disadvantage of ferrite magnets is the low coercivity field

Energies 2023, 16, 1657. https://doi.org/10.3390/en16041657 https://www.mdpi.com/journal/energies

Energies 2023, 16, 1657 2 of 23

strength. Hence, rare earth magnets are often necessary to avoid demagnetization (e.g., in a
sudden short circuit of the stator), see [6].
One alternative is the Induction Machine (IM). The benefits of IMs are robustness and
manufacturing. The rotor’s magnetic field is generated due to the induction from the stator
side. Hence, the excitation field is controlled and can also be switched off. Consequently,
there are no iron losses when the machine is switched off. Therefore, IMs are typically used
for EVs with two electrical drives. For this EVs only one machine is used for partial load.
The disadvantages of IMs are the high losses, particularly for low speed and standstill.
Controlling the IM at a standstill with high stall torque is challenging and produces losses
in the machine and inverter due to a low power factor. This operation range is relevant for
EVs in cities, e.g., starting on traffic lights, parking, etc. Furthermore, the power density of
IMs is the smallest of the discussed machine types in this article.
With Electrically Excited Synchronous Machines (EESMs), the power density is in-
creased compared to IMs while having the same benefit of an adjustable rotor excitation
due to the winding on the rotor. This machine type has been used rarely in the past in
EVs (only for Renault Zoe/Smart EQ) but is well-known as a generator (e.g., in hydro-
electric or wind power plants). BMW uses EESMs as a platform for new EVs, see [7]. The
disadvantages of EESMs are the manufacturing process of the rotor and the transmission
of the energy onto the rotor. Slip rings transmit the electrical power onto the rotating
rotor windings. In research and the literature, several concepts with a Wireless Power
Transfer (WPT) system are discussed, called Inductive Electrically Excited Synchronous
Machines (iEESMs), see [8–16]. The systems could be divided according to their operation
frequency (<20–30 kHz and >100 kHz). In several publications, only the WPT system is
investigated and could be used as a retrofit for an existing EESM to replace slip rings.
Optimization methods for EMs for EVs have been presented in the literature in recent
years for PMSMs, or PMASR [5,17–22]. In these publications, several driving cycles are
used. This depends mainly on the current valid driving cycle in the region where the work
is conducted. Sometimes several cycles or measurements are taken into account. Mainly,
the backward calculation is used: the torque requirement is derived from a given speed
with a vehicle model. The driving cycles are often reduced to a few operation points.
Compared to the presented publications, a forward model is used for this work: a
closed-loop model with a control system (driver model). The advantage is that, on the one
hand, different driver models could be used; on the other hand, the model is prepared for
use on the test bench. For the optimization, one single Representative Point (RP) in partial
load in field weakening is derived from the Worldwide Harmonized Light Vehicles Test
Cycle (WLTC) class 3. The analysis of the driving cycle is not the subject of this publication
and is therefore not discussed in further detail. The presented optimization method can also
be used with several RPs (for instance, from a mathematical reduction in the driving cycle).
In this work, a holistic approach is chosen: from the beginning, the machine and WPT
are designed and optimized as one system for the application as a traction motor for an
EV. The system is intended for use in BMW’s i3 (same mechanical power and torque) and
is optimized for high efficiency in partial load with medium speed. With this approach, a
new design of the iEESM with the integration of the WPT system inside the hollow shaft
is developed and built up as a prototype (see Figure 1). Furthermore, an electromagnetic
design optimized for field weakening is investigated, and an operation point-dependent
optimization method for EESMs is developed. The modeling of EESMs is shown and
extended. An analytical calculation method for the rotor winding factor is derived. This
factor is relevant for the calculation of the effective winding ratio, which is required for the
modeling of EESMs. The mechanical design of the machine and measurement results on
the test bench are presented.
Energies 2023, 16, 1657 3 of 23

machine stator

machine rotor
wireless power trans�er system
Figure 1. CAD model of the integrated inductive electrically excited synchronous machine.

1.1. Structure of This Article

This work starts with the modeling of the theory of modeling and operation of EESMs.
With this, the electromagnetic part of the EESM is optimized considering the RP. Further-
more, the design and construction of the WPT-system is presented. Machine and WPT are
combined, and the design and prototype of the system iEESM are presented. The iEESM is
driven on the test bench, and measurement results are shown.

1.2. Nomenclature
This work considers the machine for torque generation, the rotating wireless power
transmission and both combined. Some topics are detached from the usage, such as the
combination of machine and wireless power transmission. Issues focusing on the machine
parts, which are also valid for systems with slip rings, are named EESM (like machine
model). Topics considering the wireless power transfer itself, which could also be used
for, e.g., energy transmission for rotating sensors or sometimes even non-rotating energy
transmission, are called WPT. With iEESM, the topics considering the combination of both
are named.

2. Modeling of EESMs
This section describes the current state of modeling EESMs. An extension considering
nonlinearity is performed in previous work; see [23]. Furthermore, an analytical calculation
of the effective transformation ratio is shown. The model fastens the optimization process
and the parameter identification of the machine on the test bench: due to variable excitation,
the number of possible current combinations (current triple) is significantly larger than for
PMSMs. With the model, irrelevant combinations can be identified and do not have to be
simulated nor measured.
The model is based on the modeling of coils. They consist of resistance and inductance.
Due to the saturation, two different definitions of the inductances are used. The absolute
inductance Labs is determined by dividing the magnetic flux linkage λ through current I

λ
Labs = . (1)
I
Absolute inductances have to be used if the absolute value of the flux linkage is
necessary, e.g., for torque calculation.
Besides this, the inductance can also be calculated as a differential inductance Ldiff by
differentiation of the flux linkage as

dλ
Ldiff = . (2)
di
This definition is used if the current differentiation is necessary, especially to model dy-
namic behavior. With the neglection of the saturation, absolute and differential inductance
have the same quantity.
Energies 2023, 16, 1657 4 of 23

2.1. Modeling the EESM in dq-Frame

The EESM is modeled in a dq reference frame with the d-axis in the direction of rotor
flux and the q-axis rectangular to the d-axis (quadrature component). Due to this definition,
the rotor’s electrical excitation is on the d-axis. In the following, the voltage equation of
the EESM and the modeling as T-Equivalent Circuit (EC) are derived shortly. A detailed
description is given in [23] (also considering saturation) and [16,24].
With Clarke and Park transformation, the three-phase EESM phase voltages vabc
and phase currents iabc are transformed in dq-axis voltages vd , vq and currents id , iq ,
while the stator phase resistance is RS . The inductance in the d-axis is divided into leakage
inductance Lσd,diff and main inductance Lmd,diff , while in the q-axis both parts are combined
in Lq,diff = Lσq,diff + Lmq,diff . Saturation is considered. Hence, inductances are given as
differential inductances, and the values depend on the current. The induced voltages in the
dq-frame rely on the flux linkages λd , λq and the electrical angular velocity ω.
The effective transformation ratio aeff is defined as the ratio of mutual inductance from
the rotor to stator d-axis Lde and d-axis main inductance Lmd,abs

Lmd,abs
aeff = . (3)
Lde

Hence, the excitation current ie , voltage ve and excitation resistance Re are referred
with aeff to the stator to referred excitation current ie0 , referred excitation voltage ve0 and
referred excitation resistance Re0 . The excitation inductance is also divided into leakage and
main inductance. They are referred to the stator as excitation leakage inductance Lσe,diff 0

and main inductance Lmd,diff .

This results in the voltage equation
 
    did
vd 
RS 0

0   i d

L L L
 dt 
d,diff dq,diff md,diff 
  diq 
 vq  = 0 RS 0  iq  +  Lqd,diff Lq,diff 0   dt 

0 0
   
0
ve 0 0 Re ie0 Lmd,diff 0 Le,diff  die0 
dt
(4)
 
− ω 0  λd 
 
0
+ ω 0 0  q ,
λ 
0 0 0 λe0

with
0 2 2
Le,diff = a 2L Re0 = a 2 Re
3 eff e,diff 3 eff
ie 2 (5)
ie0 = ve0 = a ve
aeff 3 eff

Ld,diff = Lσd,diff + Lmd,diff .

Combining the currents id and ie0 in the magnetization current iµ , the equation can be
drawn as T-EC, see Figure 2.
Flux linkages can be determined with the absolute inductances Ld,abs and Lq,abs to

λd = Ld,abs id + Lmd,abs ie0 + Ldq,abs iq

(6)
λq = Lq,abs iq + Lqd,abs id .
Energies 2023, 16, 1657 5 of 23

The calculation of the electrical torque Tel is derived from Lorentz force in the dq-frame
with the number of pole pairs p to
 
Tel = 1.5p(λd iq − λq id ) = 1.5p Lmd,abs ie0 iq + ( Ld,abs − Lq,abs )id iq . (7)
| {z } | {z }
interaction reluctance

The torque is divided by its cause into interaction and reluctance torque: the interaction
torque results from the magnetic flux generated from the rotor and stator; the reluctance
torque results only from the flux from the stator.

RS Lσd,diff (iµ ,iq ) L′σe,diff (iµ ,iq ) Re′

id i′e

iµ

Lmd,diff (iµ ,iq ) ve′

vd

Ldq,diff (iµ ,iq ) i′e

id iq
−ωλq (iµ ,iq ) id − iq id − iq

id − iq
ωλd (iµ ,iq )

iq id
Lqd,diff (iµ ,iq )

vq Lq,diff (iµ ,iq )

iq RS

Figure 2. Dynamic equivalent electrical circuit in dq frame for EESMs.

2.2. Determination of the Effective Turns Ratio

The effective turns ratio aeff is necessary for modeling EESMs in T-EC and a specific
parameter of EESMs. It is often determined from measurements by shortening the stator
windings, see [23,25].
aeff is defined as the ratio of mutual inductance from the rotor to stator d-axis and Lde
and d-axis main inductance Lmd,abs , see (3). Breaking this equation down to the definition
of stator and rotor winding leads to

m Kw,S NS,coil acoils,ser 1

aeff = · , (8)
2 2 acoils,par Kw,R NR,coil
| {z } | {z }
Stator Rotor

with the number of phases m, number of windings per coils of stator NS,coil and rotor NR,coil ,
fundamental winding factor of the stator Kw,S and of the rotor Kw,R . A series connection
of rotor coils is typical and assumed. For the stator, the number of series-connected coils
acoils,ser and parallel groups acoils,par is considered.
The stator winding factor is determined by series expansion and is well-known in
the literature. The calculation of the rotor winding factor is described in the following
subsection.
Energies 2023, 16, 1657 6 of 23

2.3. Rotor Winding Factor

Ref. [25] presented an approach of an analytical determination of rotor winding factor
for EESMs with constant air-gap. In the following, a more detailed calculation method for
rotor winding factor Kw,R is derived, considering variable air-gap and rotor slot opening.
The rotor winding factor and the stator winding are calculated with the series expansion of
the air-gap flux density. The influence of the saturation as well as flux leakage is neglected.
A constant air-gap and an ideal maximum pole width results in a perfect rectangular
air-gap flux density; see the blue dashed line in Figure 3. This results in the fundamental
winding factor of 1, the maximum winding factor. This geometry is not feasible for classical
winding methods (a slot is needed) and has high harmonics. For ideal rectangular air-gap
flux density, the 5th is 20%, and the 7th is 14.2% of fundamental winding factor, which
results in high torque ripple (due to Y-wiring, the third harmonic is suppressed).
Air-gap flux density related to B̂ →

1
aPol = 1,
no tooth surface radius
0.5
aPol = 0.85,
no tooth surface radius
0
aPol = 0.85, prototype
with tooth surface radius
−0.5 rotor shape for ideal
sinusoidal flux
−1
−π / p −π /2p 0 π/
2p
π/
p

Viewing angle in the air-gap γ →

Figure 3. Air-gap flux density for different rotor shapes.

Considering the pole covering factor aPol , the winding factors are calculated with
(
sin ν a2Polν π


for ν = 1, 3, 5, . . .
Kw,R,ν = (9)
0 for ν = 2, 4, 6, . . . .

The air-gap flux density for a pole covering factor of aPol = 0.85 is plotted in Figure 3.
The fundamental winding factor is decreased to about 2.8%.
An additional rounding of the rotor tooth is used for the prototype machine to reduce
especially the fifth harmonic. In Figure 4, an example of the rounded tooth shape is shown,
and geometric variables are defined. A higher tooth rounding, as used for the prototype, is
drawn to highlight the effect of the rounding. The viewing angle-dependent γ magnetic
air-gap length δ is determined with the pole offset height hPo , the diameter of the pole
surface DR,Ps , and the stator inner diameter DS,in as
r
DS,in 2 D
δ(γ) = hPo 2 + − hPo DS,in cos(γ) − R,Ps , (10)
4 2
using the law of cosine.
With a series expansion, the odd winding factors Kw,R,ν , with the indexing variable
ν = 2, 4, ..., are determined with
π
2p aPol
Z
pδ cos(ν pγ)
Kw,R,ν = q dγ, (11)
0 DS,in 2 DR,Ps
hPo 2 + 4 − hPo DS,in cos(γ) − 2

while all even factors are zero. The equation cannot be simplified further. The analytically
determined air-gap flux density for the prototype machine is plotted in Figure 3. The
Energies 2023, 16, 1657 7 of 23

fundamental winding factor decreases to 0.696, but the fifth harmonic is decreased to 4.3 %
of the fundamental winding factor. This directly reduces torque ripple.

γ=π/2p aPol
γ=π/2p
γ=π/2p aPol
2 X
D S,in/ X
s δ(γ) δ(γ)
D R,P
/2 /2
D S,in s
D R,P
γ γ
γ=0
CS hPo CP
δmin

Figure 4. Sketch of a rotor tooth with additional radius with the parameters: rotor pole covering factor
aPol , air-gap height δ, pole offset hPo , rotor pole surface diameter DR,Ps , stator inner diameter DS,in .

An academic approach for an ideal sinusoidal air-gap flux density is presented in [26]
(p. 170ff). Considering the pole covering factor, the fundamental winding factor is deter-
mined with

1
Kw,R =
(πaPol + sin(π aPol )). (12)
4
All even harmonics are zero and all odd harmonics ν = 3, 5, . . . are calculated with

ν cos(0.5 π aPol ) sin(0.5 π ν aPol ) sin(0.5 π aPol ) cos(0.5 π ν aPol )

Kw,R (ν) = − . (13)
ν2 − 1 ν2 − 1
The air-gap flux density is plotted in Figure 3 for aPol = 1.

3. Optimization for Field Weakening

In this section, the influence of the rotor shape on high efficiency in field weakening
is shown.

3.1. Operation of EESMs in Field Weakening

There are several operation strategies for EESMs. The most popular ones are Maximum
Torque Per Ampere (MTPA), where the copper losses are reduced, and Maximum Efficiency
(ME), where the overall losses of the machine are reduced, including iron losses. Due to
the excitation current, there is one additional degree of freedom for EESMs compared to
PMSMs. Hence, MTPA needs an additional condition to be solvable. Ref. [27] shows several
possibilities for an analytic determination neglecting iron saturation. For applications with
high power and torque density, such as traction drives for EVs, the impact of saturation
has to be considered. Hence, a model with current-dependent Lookup tables (LUTs) for the
inductances has to be used and numerically solved. A simplified approach is used below
to highlight the principles and opportunities for influence.
Energies 2023, 16, 1657 8 of 23

Field weakening is the operation at the stator voltage limit v̂max which leads to
q
v̂max = vd 2 + vq 2 . (14)

Considering stationary operation and neglecting the resistances, (4) is simplified

with (6) into
 2
v̂max
2
= λd 2 + λq 2 = Ld,abs id + Lmd,abs ie0 + Lq,abs 2 iq 2 . (15)
ω

For simplification, the analysis is conducted for a rotor without saliency (L = Ld,abs
= Lq,abs ). The leakage flux (Lmd,abs = Ld,abs = L) is neglected because the purpose is to
look at and explain the principle of field weakening of EESMs. With this supposition, the
voltage equation results in
 2
v̂max
= L2 (id + ie0 )2 + L2 iq 2
ω
(16)
 2
v̂max
= (id + ie0 )2 + iq 2 .
ωL

With (7), the output power, considering the previously shown simplifications, is
determined with
Pmot = 2π T n = 1.5 ω L iq ie0 . (17)

3.1.1. Field Weakening by Reducing the Excitation Current

An evident opportunity for achieving field weakening for EESMs is the reduction in
the rotor current. However, this is not the optimal solution since the field weakening is
limited, as derived below.
For a rotor without saliency, there is no reluctance torque. Hence, id = 0 and iq = îmax
in base speed. When the voltage limit is reached, the (referred) excitation current ie0 has
to be reduced. The excitation current depending on the electrical frequency ω = 2 πn is
derived with (16) into
r r
0 v̂max 2 2
v̂max 2
ie ( ω ) = − i q − i d = − îmax 2 . (18)
L2 ω 2 |{z} L2 ω 2
=0

This condition inserted in (17) leads to

q
Pmot = 1.5 îmax v̂max 2 − îmax 2 L2 ω 2 . (19)

The output power Pmot is zero for v̂max 2 = îmax 2 L2 ω 2 , which results in the maximum
speed of
v̂max
nmax = . (20)
2 π L î
max
As a result, field weakening due to the reduction in the excitation current leads to
limited field weakening and a non-constant power in field weakening. In Figure 5, currents,
torque, power and voltage are plotted over speed. The variables are related to the corner
point (operation point, where the voltage limit is reached with maximum stator current
and referred excitation current ie0 = îmax ). In addition, the bottom graph also shows the
power factor (pf). With the method of reducing the excitation current, the power factor
decreases significantly in field weakening.
Energies 2023, 16, 1657 9 of 23

2 2

current →

mech. power / torque→

1.5 i′e iq id Pmot T
1.5
1
0.5 1
0
0.5
−0.5
−1 0
0 1 2 3 0 1 2 3
1.5 normalized speed n→
voltage / pf →

pf = cos(θ) VS

1
iq = îmax , i′e ̸= const.
i′e = îmax = const.
i′e = 2 îmax = const.
0.5
i′e = 1/2 îmax = const.

0
0 1 2 3
normalized speed n→

Figure 5. Influence of field weakening on electrical and mechanical quantities over speed for different
field weakening approaches. Upper plot shows the influences on current, the middle plot on output
power and torque and the bottom plot shows speed-dependent voltage and power factor. The color
indicates the discussed method (see upper legend), and the line style indicates the quantity (shown
in the legend in each plot). The quantities are related to its value on the corner point for the first
approach (ie0 = îmax = const.). For all approaches, the magnitude of the stator current is maximum
(îmax ). All losses are neglected.

3.1.2. Field Weakening by Negative d-Axis Current

The other opportunity to achieve field weakening is to weaken the field from the stator.
This is achieved with a negative d-axis current id . With (16) the d-axis current depending
on the electrical frequency ω is derived into
r
v̂max 2
id ( ω ) = − iq 2 − ie0 . (21)
L2 ω 2
q
The stator current is set to îmax = id 2 + iq 2 to achieve maximum torque. This results
in a speed-depended q-axis current to
v
u r !2
v̂max 2
q u
iq ( ω ) = îmax − id (ω ) = tîmax 2 −
2 2 − iq 2 − ie0 . (22)
L2 ω 2

In the following, a closer look at the case ie0 = îmax is taken, which can be reduced. The
common case will be considered numerically later. This condition leads to
p
v̂max 4îmax 2 L2 ω 2 − v̂max 2
iq ( ω ) =
2îmax L2 ω 2

and is combined with (17) to obtain

r
v̂max v̂max 2
Pmot (ω ) = 1.5 4îmax 2 L2 − . (23)
2L ω2
Energies 2023, 16, 1657 10 of 23

The first finding is that for high speed, the power is constant:
ω →∞
Pmot (ω ) −−−→= 1.5 îmax v̂max . (24)

Secondly, the power is increasing until |ω |  v̂max .

This behavior is good for machines with a wide field weakening area, such as traction
motors for EVs.
In Figure 5, the currents, torque, power, voltage and power factor are plotted over
speed. The variables are related to their value at the corner point. The blue line
q shows the
result for the previously derived optimal condition: ie0 = îmax = const. and id 2 + iq 2 =
îmax . It can be shown that the power factor also increases in field weakening. Hence, the
maximum power in field weakening is higher than at the corner point.
As an example, the conditions ie0 = 2 îmax = const. (red) and ie0 = 1/2îmax = const.
(purple) are plotted. With higher excitation current, the torque and power in base speed
can be increased, but the field weakening is strongly limited. Reduced excitation current
can increase the field weakening, but output power is reduced, and field weakening is also
limited. In both cases, the power factor increases in field weakening. All shown evaluations
are conducted without the consideration of any losses. The iron, bearing and air friction
losses are highly speed-dependent for real machines. Hence, the output power decreases at
a certain speed, and the maximum speed is limited. Nevertheless, the shown conditions
regarding power factor and maximum theoretical speed apply.

3.1.3. Conditions for Infinite Field Weakening

In sum, the current triple for constant power in field weakening is calculated with

ie0 = îmax

v̂max 2 v̂max 4
   
1
iq = − (25)
Lω 4 îmax 2 Lω
q
id = − îmax 2 − iq 2 .

The finding of this derivation is that, even when the rotor flux is adjustable, a negative
d-axis current is necessary to reach constant power in field weakening. For real machines,
d-axis and q-axis inductances are different. The rotor of EESMs is most salient due to the
winding on the rotor tooth. Hence, typically Ld,abs > Lq,abs . Combing torque calculation (7)
with the current definition in field weakening (25) leads to a negative reluctance torque

( Ld,abs − Lq,abs ) iq id < 0. (26)

| {z } |{z} |{z}
>0 >0 <0

In summary, d-axis inductance should be smaller than q-axis inductance

Ld,abs < Lq,abs . (27)

Another result is that in field weakening operation the referred rotor current ie0 is in
the range of the stator current î—especially at the maximum characteristic. The analytical
calculation of aeff , presented in Section 2, is helpful in the design process. Due to flux
leakage, nonlinearity and various loss effects, ie0 does not necessarily need to be the same as
î for optimal operation (e.g., maximum efficiency operation).
Ref. [23] shows that this also has a positive effect on the operation below field weak-
ening. Due to the saturation, the negative d-axis current desaturates the main inductance
Lmd,abs . It leads to an increase in interaction torque.
Energies 2023, 16, 1657 11 of 23

3.2. Rotor Design for Ld,abs < Lq,abs

As previously described, the condition Ld,abs < Lq,abs is suitable to achieve high
efficiency in field weakening as well as in operation with high torque (due to saturation).
Due to the rotor winding, d-axis inductance is typically higher than q-axis inductance for
EESMs. In the following, it is shown that this ratio can be turned due to the saturation in
the rotor. Therefore, a closer look at the rotor flux density is taken. The frozen permeability
method is used to divide the flux into its cause. It is a pure theoretical method to explain
the influence of different magnetic sources on a saturated magnetic part, see [28,29]. The
permeability from one simulation is “frozen” and used for another simulation.
Simulations with rotor current but without stator current are used to determine the
permeability. The permeability in the rotor yoke (marked with blue in Figure 6a) is then
used for a simulation with only stator current. The current is set to iq = −id = 150 A. With
this combination, it is expected that the ratio of Ld,abs to Lq,abs can be displayed as
Ld,abs > Lq,abs the main flux path is in d-axis direction;
Ld,abs ≈ Lq,abs flux path is approximately halved into d-axis and q-axis direction;
Ld,abs < Lq,abs the main flux path is in q-axis direction.

1000
q
Simulation with rotor but

Relative Permeablity μr
without stator current

600
300
1
q

μr trans�erred and �ixed μr trans�erred and �ixed μr trans�erred and �ixed μr trans�erred and �ixed

2.5 2
Simulation without rotor
but with stator current

Flux density in T
1
0
(a) Principle o� (b) iE= 0.5 A (c) iE= 5 A (d) iE= 10 A
the method

Figure 6. Simulation with frozen permeability method for different excitation currents. (a) Shows
the principle of the method: simulations on the top are performed without stator current. The
permeability in the marked region is frozen and used for the simulation with stator but without rotor
current. (b–d) Shows the permeability of the iron without stator current (left) and the resulting flux
density considering stator current (iq = −id = 150 A, ie = 0 A). On the bottom side, the flux density
vector is plotted in red. Additionally, the preferred flux paths are highlighted with black arrows.

Due to the low excitation current in Figure 6b, the permeability of the rotor yoke is
high, and the main flux path is through the rotor yoke. This means that the main flux path
is in the d-axis direction, and hence, Ld,abs > Lq,abs . The excitation current in Figure 6c is
chosen to picture the region where Ld,abs ≈ Lq,abs . It can be seen that there is no clear main
path. The flux path is divided into one part through the rotor yoke (d-axis direction) and
one part which dives only into the tooth tip and exits the tooth near the q-axis. In Figure 6d,
the excitation current is further increased. The main part of the magnetic flux shortens the
rotor from the d-axis directly into the q-axis. The amount of stator flux through the rotor
yoke is low. In this case, Ld,abs < Lq,abs . In Figure 7, the inductances and torque depending
on ie are plotted. The results agree with the description of Figure 6. At approximately
ie = 5.5–6 A, Lq,abs is higher than Ld,abs and torque-determined only with stator current is
Energies 2023, 16, 1657 12 of 23

becoming positive. It is also evident that for ie < 2 A, the torque is negative, even if the
rotor excitation is considered.

Inductance in µH→

Torque in Nm→
800 Ld,abs
100
Lq,abs
600
400 0
Tel (ie > 0A)
200 Tel (frozen permeability)
0 −100
5 10 15 20 5 10 15 20
ie (for saturation) in A→ ie (for saturation) in A→

Figure 7. Inductances over excitation current ie determined with frozen permeability method. The
bottom figure shows torque with and without excitation current. Stator current is set to iq = −id = 150 A
for all simulations.

In summary, the d-axis inductance could be smaller than Lq,abs , even for EESMs. The
rotor tooth has to be designed so that the yoke and tooth (d-axis flux path) are saturating
in a wide range of ie . The simulations are performed with the build-up prototype. It is
designed for a maximum excitation current of ie = 20 A. Above a current of ie ≈ 5 A, the
rotor yoke saturates and Ld,abs is smaller than Lq,abs . This is achieved due to a bottleneck
for the rotor tooth’s magnetic flux, which starts to saturate first; see Figure 6c. Second, the
yoke saturates; see Figure 6d. Additionally, the tooth tip width has to be high (small slot) to
increase Lq,abs . The above requirements are unfavorable for the mechanical strength of the
tooth. Hence, EESMs often have a high tooth width and rotor yoke to increase mechanical
strength, especially in generator designs. Therefore, the mechanical strength of the design
machine is analyzed before manufacturing the prototype.

4. Electromagnetic Optimization of the Machine Parts

This section shows the electromagnetic optimization of the EESM. An operation
point-dependent optimization method for EESM is developed and applied to an EESM
as traction drive for a medium-sized EV. The goal is to optimize the 2D design of the
electromagnetic parts.

4.1. Optimization Method

For the optimization, two optimizations are nested, as shown in Figure 8. The outer
optimization is the geometry optimization. A multi-objective Non-Dominated Sorting
Genetic Algorithm (NSGA) is used to vary the geometry and find the best solution. The
costs are calculated for each individual, generated with NSGA. The optimization goal is to
achieve high efficiency at one operation point (even several operation points are possible)
and to reduce torque ripple for this operation point. Furthermore, there are a few hard
constraints that have to be fulfilled. At first, the hard constraints are verified. Therefore,
MTPA with maximum current is solved numerically by combining the analytical model
shown previously and Finite Element Analysis (FEA). To reduce simulation time, at first,
one FEA is solved with iq = îmax and ie = ie,max and the inductances are derived. With these
inductances, MTPA is solved with the analytical model. The resulting current combination
is used for another FEA, and the analytical modeling is repeated. For the applied optimiza-
tion, less than five FEA are sufficient to determine MTPA with the maximum current. The
rated point is selected due to the voltage limit with simulated inductances. Power and
torque are compared with hard constraints.
Energies 2023, 16, 1657 13 of 23

Geometry
Operation point
Geometry
optimization and
optimization
cost calculation
Costs

• Optimize geometry • Hard constraints

inside boundaries - Determine Tmax and Pmax
• Achieve less - Calculate weighting (0-1)
cost with • Current optimization for
multi-objective operation point
optimization - Cost 1: Weighted efficiency
- Cost 2: Weighted Torque
ripple
Figure 8. Overview of the nested optimization.

Next, the efficiency of the operation point is determined. This also requires an opti-
mization of the current triple. A combined analytical model and FEA is used. Furthermore,
less than five FEAs are necessary to determine efficiency. Iron losses are neglected in
calculating the currents but are considered in the efficiency. Besides efficiency, torque ripple
in the operation point is determined.
The resulting costs (efficiency and torque ripple) are weighted due to the hard con-
straints. If an individual is far from the constraints, costs calculation aborts before operation
point optimization, and the worst value for the cost is submitted. If the constraints are
nearly reached, efficiency in the operation point is determined, but both costs are weighted.
Hence, efficiency is reduced, and torque ripple is increased.

4.2. Applied Optimization

The requirements and boundary conditions are derived from the BMW i3 as reference
EV. The main requirement is to achieve the same operating range as the PMSM used
in the i3. Furthermore, the electrical conditions are the same. Due to the construction
and manufacturing, the outer diameter, active length and the number of pole pairs are
fixed. The optimization goal is to achieve high efficiency, especially for medium-to-high
speed in partial load. As RP, an operation point with 40 Nm at 9000 rpm was chosen. The
optimization’s main boundary conditions and goals are listed in Table 1.

Table 1. Main conditions for optimization.

Requirements Operation Point Optimization

Rated torque 150 Nm Speed 9000 rpm
Maximum torque >250 Nm Torque 40 Nm
Rated speed 4800 rpm Machine efficiency maximize
Maximum speed 11,400 rpm Torque ripple minimize

The optimization results for torque ripple and efficiency are shown in Figure 9. As an
example, the results for the 5th, 15th, 24th and 28th generation are plotted. The blue line
shows the Pareto front (no individual achieves lower costs for both cost functions). From
5th to 12th and also to 24th, the individuals become better. For the 5th and 12th generations,
the individuals achieve either high efficiency or low torque ripple. With the 24th generation,
both can be achieved. Simulation is aborted after the 28th generation because results could
not be improved significantly. The marked individual is chosen for the prototype due to
low torque ripple Tshaft∼ and good efficiency ηOP . The efficiency could not be increased
significantly. The result seems robust because several individuals achieve similar results.
Energies 2023, 16, 1657 14 of 23

97.4
Generation 5
Generation 15
Generation 24

ηOP in % →
Generation 28
97.2 Pareto front
Selected
Selected

97
3.5 4 4.5 5 5.5 6 6.5
Tshaft∼ in Nm→
Figure 9. Optimization results; selected geometry for prototype is highlighted.

4.3. Electromagnetic Simulation of the Finalized Geometry

In Figure 10a, the flux density of the prototype machine at the optimization point
(40 Nm@9000 rpm) is shown. This operation point is in partial load and field weakening.
The flux density is about 1 T and becomes more saturated for higher torque.

1.9
300 96
T in Nm→

80
85 operation point
1.5 250
for efficiency

η in % →
92
B in T→

200 optimization
96
9920

1.0
94
95
150 96 88
880
5

100 97 95
0.5 84
97

50
80
0.0 1000 3000 5000 7000 9000 11000
n in 1 /min →

(b)
(a)
Figure 10. Simulation results of the optimized machine. (a) Flux density for prototype machine
for 40 Nm@9000 rpm, (b) Simulated efficiency map for prototype machine considering copper and
iron losses.

The complete simulated efficiency map for the prototype machine is shown in Figure 10b.
The representative point is marked. During optimization, efficiency at this point is increased.
This point is in the area of maximum efficiency of >97%. The region with efficiency >97%
extends from 5000 rpm up to 9500 rpm and up to 50% of maximum torque (at 7000 rpm).
As the mechanical losses are neglected, it is to be expected that the measured efficiency is
slightly lower. The influence of the mechanical losses depends on the speed. The effect
on efficiency is higher at low-to-medium loads than at high loads. Due to the fact that
mechanical losses cannot be optimized with the active parts, neglecting mechanical losses
is permissible for optimizing the electromagnetic parts.

5. Design of the WPT System

For the WPT system, a both-sides compensated system is used to achieve a good effi-
ciency. The equivalent circuit is shown in Figure 11. On the primary side, the compensation
(Cprim ) is in series to the inductance (Lprim ). On the secondary side, the compensation (Csec )
is parallel to the inductance (Lsec ). M is the mutual inductance between (Lprim ) and (Lsec ).
The system is driven with a DC source on the primary side.
The system is designed according to [30], the topologies are described in [15]. For
the operation of the WPT system, a full bridge inverter is used on the primary side and a
half bridge active rectifier is used on the secondary side. With the both-sides compensated
system and the active rectifier, a maximum efficiency of more than 95% of the WPT system
is achieved in the best operating point. The efficiency includes the losses of the inverter and
Energies 2023, 16, 1657 15 of 23

rectifier, but it neglects the losses in the variable voltage source, which is used to control
the rotor current. The WPT system has a wide operating area due to the temperature-
depending rotor resistance. The system is designed so that the maximum efficiency is
reached at higher rotor resistances to reduce the losses in the hot operating points.

Cprim M
= ~
Lsec Csec
Lprim Re

~ =
Inverter Rectifier

Figure 11. Equivalent circuit of the WPT system.

6. Construction of the Prototype

This section describes the construction of the iEESM as a complete system. It starts
with the WPT placement of the WPT. Next, the design of the rotor is shown and ends with
the construction of the complete iEESM. An excerpt of the prototype’s parameters is listed
in Table 2.

Table 2. Parameters of the prototype and the BMW i3.

Prototype BMW i3 [31]

Number of pole pairs p 4 6
Stator outer diameter DS,out 230 mm 242 mm
Rotor outer diameter DR,o 179 mm 179 mm
Stack length lstack 180 mm 132 mm
Magnetic air-gap length δ 0.5 mm 0.5 mm
Number of stator slots QS 48 72
Tshaft for line peak current 530 A 310 Nm 250 Nm
Torque density at maximum torque point 41.4 kNm/m3 41.1 kNm/m3

6.1. Placement of the WPT

Figure 12 shows the possibilities for the placement of the WPT system. The Drive
End (D.E.) of the machine is on the left side and the Non-Drive End (N.D.E.) on the right side.

Option C
Option A
Option B2

Option B1

Figure 12. Possibilities for placement of the WPT system.

Option A (outside on the N.D.E.) is predestinated to replace slip rings of an EESM

and is used in [15,16]. The additional space compared to PMSMs and the need for one or
two bearings in the WPT system are disadvantageous.
Energies 2023, 16, 1657 16 of 23

Option B (Inside beneath the stator end windings) is often used in current publica-
tions [9,10,15,16,32]. Typically, variant B1 with the transmission on the N.D.E. is used
because no torque is transmitted on this side. It is also easier to mount and contact. In most
cases, this side is the one with the floating bearing. Hence, the manufacturing tolerances
and thermal expansion have to be considered in the design process of the WPT system.
Furthermore, air cooling for the rotor winding has to be considered. This can be a challenge
for rotationally symmetric systems.
Option C (inside the shaft) is a novel option invented during the development of the
presented iEESM. The placement of an energy transmission system inside the hollow shaft
is patented in [33,34]. The WPT system is integrated into the machine shaft. The advantage
is that spare space is used, and the dimensions of the complete system iEESM only depend
on the machine parts. The requirement is that the diameter of the rotor is correspondingly
large. The space in the hollow shaft must be sufficient for the transmission system. In this
option, the WPT system does not influence a rotor winding air cooling. In turn, the cooling
of the WPT system must be considered.
The WPT system has to be designed with an outer rotating secondary side fixed and
mounted inside the shaft. The stationary primary side is placed on a rod or tube inside the
secondary side.

6.2. Rotor Construction

Figure 13a shows the rotor construction of the machine parts. Several parts increase
the mechanical strength of winding and end winding. An aluminum end winding mount
is added directly to the electrical sheet on both sides. Teeth are covered with a PEEK end
winding wire guiding. Hence, the first layer of rotor winding is guided to receive proper
winding. The end winding mount on D.E. is bandaged with an aluminum star. Due to the
WPT, electronics mounted on N.D.E., a Glass-Fiber Reinforced Plastic (GFRP) is used on
that side. For winding fixation, a GFRP wedge is added into the slot after wounding, and
the complete rotor is impregnated with a resin.

D.E.
D.E. Sha�t Secondary side winding
end winding
end winding Rotor (Steel E295) Primary side winding
bandaging (Al)
mount (Al) lamination Resolver
(M235-35A)
Primary side tube
N.D.E.
end winding
mount (Al)

End winding
wire guiding
Fan mounting
(PEEK)
Bearings
N.D.E. IR Sensor Shaft Grounding CET electronic
end winding Ring with heatsink
bandaging (GFRP) (a) Construction o� the rotor (b) Construction o� the iEESM
Figure 13. Mechanical design of the rotor (a) and the complete iEESM (b) in a cross-sectional view.

Figure 14 shows the integration of the WPT system for the prototype.
Energies 2023, 16, 1657 17 of 23

(a) End winding bandage and (b) End winding

end winding bandage o� D.E. bandage o� N.D.E.

(a) Rotor assembly, (b) Rotor winding o� the (c) Rotor assembly with
view �rom D.E. WPT system PT100, view �rom N.D.E.

(d) Rotor assembly with (e) Rotor assembly with CET (�) Stator winding o� the WPT
CET coils and heat sink coils, heat sink and PCB system (N.D.E. on th le�t)
Figure 14. Integration of the WPT system of the prototype at different manufacturing states.

6.3. iEESM Construction

Figure 13 is a cross-section of the complete system in an axial direction. The rotor
is mounted inside the stator with two bearings. A shaft grounding is added on the D.E.
to avoid bearing currents. As a position sensor, a four-pole resolver is used. For rotor
temperature measurement, Infrared (IR) sensors sense rotor end winding temperature
from the stator. The WPT stator consists of a wound PEEK tube that could be cooled with
compressed air. Alternatively, the primary side could be redesigned for water coolant. On
the N.D.E., the fan for ventilation is mounted with a 3D-printed part.

7. Prototype, Control and Measurement

This section describes the control of the iEESM, the test bench setup and measurement
results.

7.1. Control
Figure 15 gives an overview of the control system of the iEESM.

ie, SP
WPT Controller with WPT
Rotor Current Controller Power Elektrconic

uLimit,v

vabc(t) Resolver
Tref + vdq,SP
idq, SP +
nmeas idq, err +
− εel,k+1 vabc, SP
Current control with Space Vector
Operation
anti-windup Modulation
strategy Coupled
εel,k → εel,k+1 Inverter Stator Rotor
ie, SP and Limiter Coils
vdq, ind
d/q-decoupling
PWM iEESM
Decoupling iabc (t)
iabc
abc Current
idq,meas dq Measurement
εel
sin(εel(t))
nmeas PLL cos(εel(t))
real time software for machine control

Figure 15. Real-time software for machine control (highlighted in gray) with in- and outputs. Big
arrows are vectors with multiple signals; small arrows show single signals.

The input variable for the machine control is the reference torque Tref . The operation
strategy defines the speed-dependent setpoint currents for stator idq,SP and rotor ie,SP . The
induced voltages vdq,ind for decoupling the d- and q-axis are calculated with setpoint
Energies 2023, 16, 1657 18 of 23

currents and measured speed. Subtracting measured stator current idq,meas from idq,SP
results in the current error idq,err and is one input for the current controller. The second
input is a flag to enable anti-windup if the voltage limit is reached. If the voltage limit is
reached, integration is stopped. The current controller is realized as a PI controller. The
addition of the output from the current controller and induced voltages results in setpoint
voltages vdq,SP . They are transformed into three-phase Pulse Width Modulation (PWM)
signals vabc,SP with space vector modulation and the estimated electrical angle of the next
time step ε el,k+1 . The PWM signals are input for the inverter to result in the physical
three-phase voltages vabc (t). The second output from space vector modulation is a flag
to indicate whether the voltage limit is reached to start the anti-windup method. The
three-phase currents iabc (t) are measured and transformed into dq-currents idq,meas . The
electrical angle ε el and speed nmeas are measured with the resolver and determined with a
Phase-Locked Loop (PLL).

7.2. Test Bench Setup

Figure 16 shows the setup on the test bench at the Institute of Electrical Energy Conver-
sion (IEW). The test bench is driven speed-controlled, and the iEESM is torque-controlled.
The power is measured with HBM’s power meter GEN7tA. The machine is operated with
Semicron’s three-phase voltage source inverter SKAI 45 A2 GD12-WQI. Except for the
current measurement, the inverter used is the same as [35]. dSPACE’s scalexio system is
used to realize the control system, consisting of a processing unit and a LabBox (for IOs).

Test bench CET Inverter

Dynanometer Excitation
(IEW)
Measurement current
System under test set point
Power 1=

DC power supply
Data
Torque
sensor 1~ Inverter (SKAI)
mechanical 1=
power
3~
estimated
Duty AC currents, excitation
cycles DC voltage current
iEESM dSPACE Scalexio
speed, Processing unit + LabBox
position

Machine AC power
Power meter
(GEN7tA) Machine DC power
CET DC power
Figure 16. Test bench setup.

7.3. Measurement Results

The measurements are taken at static load with constant temperature (stator copper
temperature 50–70 ◦ C, temperature of the rotor winding and WPT coil system 70–90 ◦ C).
In Figure 17, the measured flux linkage maps are plotted over magnetization current
iµ and q-current iq . Regarding Section 2, the number of measured operation points is
reduced significantly. Only id -ie -combinations with positive magnetization current iµ are
measured because negative magnetization is irrelevant. Furthermore, operation points with
Energies 2023, 16, 1657 19 of 23

low q-current iq and high magnetization current iµ are not optimal. Hence, only operation
points with iq/iµ ≥ 0.5 are measured.
The saliency ratio Lq,abs/Ld,abs is plotted as an example for ie = 7 A and ie = 11 A in
Figure 18a,b. It shows that for both excitation currents, the q-axis inductance is greater than
the d-axis inductance (Ld,abs < Lq,abs , saliency ratio ≥1) for most current combinations. As
described in Section 2, this positively impacts the efficiency of field weakening operation. A
maximum saliency ratio of 2.5 is achieved. The saliency ratio increases with the excitation
current. This is consistent with the theoretical investigations and the optimization shown
in this work. Additionally, in Figure 18c,d, the measured absolute inductances Ld,abs and
Lq,abs are visualized. Lq,abs is mainly depended on iq while Ld,abs is more or less constant.
The d-axis inductance is mainly saturated due to the excitation current ie = 11 A (maximum
is ie = 20 A).
90
100100 90
90 90
200

80
90
λ in mWb

80
70
iq in A→

80 80 60
0
50 90 9 60
60

100
60

8080 40
30
2020
60

20
60

10
100 200 100 200
iµ in A→ iµ in A→
(a) Main flux linkage (b) Flux linkage
in d-axis λmd in q-axis λq

Figure 17. Measured flux linkages at 2000 rpm.

1.0
2.5 250
1.25
1.00
2.50
1 .0
Saliency ratio

1.5
2
0

150 3
200
iq in A→

iq in A→

1.25
2.00

0
1.50

4.
3.00

1.5
2.5
.25

2.0
4.00

1.5 1
100
1.25

1.25

1.00

1.00
1.25
2.50

1.5
150
1 2.0
50 2 .0
1.50
2.00
3.00

2 .0 2.5
1.25

2.5
100
−160 −140 −120 −100 −80 −60 −40 −150 −100 −50 2.5

2.5
id in A→ id in A→
(a) ie =7A (b) ie =11A
100

250 250
Inductance in µH

30
500

0
500
0

200 200
300
iq in A→

iq in A→

10
200

500 500
300
30

500
0

300 150 150

300

600 600
0 600
30
300

200

100 100 100

−150 −100 −50 −150 −100 −50
id in A→ id in A→
200

(c) Ld,abs (ie =11A) (d) Lq,abs (ie =11A)

Figure 18. (a,b) Saliency ratio Lq,abs/Ld,abs exemplary for two constant excitation currents, (c,d) absolute
inductances Ld,abs and Lq,abs for ie = 11 A.
Energies 2023, 16, 1657 20 of 23

The measured efficiency with the operation strategy MTPA is shown in Figure 19.
Highest efficiency is in partial load 50–100 Nm for 2500–4000 rpm. The efficiency of the
iEESM is more than 92% for speed above 1500 rpm. The maximum efficiency for the entire
drive (including the machine inverter) is 92.5% in a wide range above 2500 rpm.
The measurements are compared with the results of BMW’s i3 PMSM of [31]. The
efficiency of the iEESM is higher in nearly all operation points and is more than 4 percentage
points higher for a broad region. As expected, the efficiency difference is at its maximum in
partial load.
In Table 3, selected measurement results are listed. The effective turns ratio is deter-
mined with short circuit measurements with different excitation currents (as described
in [23]).

Table 3. Measurement results.

Efficiency iEESM 50–75 Nm@2500–4000 rpm 95%

Efficiency of reference PMSM for 50–75 Nm@2500–4000 rpm 90–92% [31]
iEESM linearized inductance Ld,abs (ie ) = 11 A ≈300 mH
iEESM linearized inductance Lq,abs (ie ) ≈600 mH
iEESM effective turns ratio 1/18.6 = 0.0538

(a) iEESM efficiency ηiEESM (b) Drive efficiency ηDrive

150 92 90
96
Tshaft in Nm→

125 94
90

η in %
95

100 92

92
94
75 95 90 90
92

50
95 88
90 92
94 92 86
25 92 90
94

90 90
150 999245 904 95 90
94
Tshaft in Nm→

92
8
125
92 2 6
100 2

∆η in %
90

4 4
75 4
2 2
90
50
6 0
25
6

4 2 6
4 −2
1000 2000 3000 4000 1000 2000 3000 4000
642 2

nEM in rpm→ nEM in rpm→

(c) Reference PMSM (d) Difference efficiency
efficiency ηPMSM ηiEESM − ηPMSM

Figure 19. (a,b) measured efficiency with operation strategy MTPA on the test bench, (c) results from
reference PMSM [31], (d) difference in efficiency ηiEESM − ηPMSM .

8. Conclusions
This publication presents the process of designing, modeling, optimizing, constructing
and measurement of an iEESM.
The system iEESM consists of the machine part for torque generation and the wireless
power transmission onto the rotor. It is designed for use in an EV. For the reference vehicle,
BMW’s i3 was chosen. A wide operating range is therefore required. In particular, the part-
load zone is relevant for high efficiency in the drive cycle and an extended vehicle range.
Hence, this work focused on the design of the iEESM in field weakening and high
integration of the WPT. The WPT is placed inside the hollow shaft, reducing the necessary
space for the system. The rotor is designed to achieve positive reluctance torque with negative
Energies 2023, 16, 1657 21 of 23

d-axis current. This work argues that this is necessary for operation in field weakening
with a wide constant power range. It is proven with measurements of the inductances. The
measurement results of the efficiency of the iEESM were compared with the measurements
of the i3’s PMSM. The efficiency is significantly increased by about 4 percentage points in a
wide operation range and up to 8 percentage points in single operation points.

9. Patents
Two patents result from this work, see [33,34].

Author Contributions: Conceptualization , software and validation, S.M. and D.M.; methodology,
software, validation of the machine parts and validation of the complete system, S.M.; methodology,
software and validation of the wireless power transmission system, D.M.; supervision and discussion,
S.M., D.M, and N.P. All authors have read and agreed to the published version of the manuscript.
Funding: The research leading to this publication has received funding from the Vector Stiftung in
Stuttgart. https://www.vector-stiftung.de/ (accessed on 4 February 2023).
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:

BMW Bayerische Motoren Werke AG

D.E. Drive End
EC Equivalent Circuit
EESM Electrically Excited Synchronous Machine
EM Electrical Machine
EV Electrical Vehicle
FEA Finite Element Analysis
GFRP Glass-Fiber Reinforced Plastic
iEESM Inductive Electrically Excited Synchronous Machine
IM Induction Machine
IR Infrared
LUT LookUp Table
ME Maximum Efficiency
MTPA Maximum Torque Per Ampere
N.D.E. Non-Drive End
NSGA Non-Dominated Sorting Genetic Algorithm
PLL Phase-Locked Loop
PMASR Permanent Magnet-Assisted Synchronous Reluctance Motor
PMSM Permanent Magnet Synchronous Machine
PWM Pulse Width Modulation
RP Representative Point
WLTC Worldwide Harmonized Light Vehicles Test Cycle
WPT Wireless Power Transfer

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