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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 3, SEPTEMBER 2012
A Multilayer 2-D–2-D Coupled Model for Eddy
Current Calculation in the Rotor of an Axial-Flux
PM Machine
Hendrik Vansompel, Peter Sergeant, and Luc Dupré
Abstract—On the rotors of an axial-flux PM machine, NdFeB
permanent magnets (PM) are very often placed because of their
high energy density. As the NdFeB-magnets are good electric conductive, electric currents are induced in the magnets when they are
exposed to a varying magnetic field. This varying magnetic field
has two causes: variation of the airgap reluctance due to the effect
of stator slots and armature reaction due to the stator currents.
As axial-flux PM machines have an inherent 3-D-geometry, full
3-D-finite-element modeling seems necessary to calculate the eddy
currents in the PM and to evaluate their corresponding losses. In
this paper, however, the 1-D airgap magnetic fields of multiple multilayer 2-D finite-element simulations are combined to a 2-D airgap
magnetic field using static simulations. In a subsequent step, this
2-D airgap magnetic field is imposed to a 2-D finite-element model
of the PM to calculate the eddy currents and eddy current losses.
The main benefit of this multilayer 2-D–2-D coupled model compared to 3-D finite-element modeling is the reduction in calculation
time. Accuracy of the suggested multilayer 2-D–2-D coupled model
is verified by simulations using a 3-D finite-element model.
Index Terms—Armature reaction, axial-flux machine, eddy currents, finite-element methods, permanent magnet (PM) generators,
permanent magnets (PM).
I. INTRODUCTION
ECAUSE of their high energy density, NdFeB permanent
magnets (PM) are very often placed on the rotors of an
axial-flux PM machines in order to obtain high power-to-weight
ratios and high efficiencies [1]. However, as the NdFeB-magnets
are good electric conductors, electric currents are induced in the
magnets when they are exposed to a varying magnetic field. This
varying magnetic field has two causes: variation of the airgap
reluctance due to the effect of stator slots and armature reaction
due to the stator currents. The induced eddy currents result in
B
Manuscript received December 23, 2011; revised February 22, 2012; accepted March 25, 2012. Date of publication May 8, 2012; date of current
version July 27, 2012. The research was supported by the Research Fund of the
Ghent University (BOF-associatieonderzoeksproject 05V00609), by the Fund
of Scientific Research Flanders (FWO) under Project G.0082.06 and Project
G.0665.06, by the GOA project BOF 07/GOA/006, and the IAP project P6/21.
Paper no. TEC-00668-2011.
H. Vansompel and P. Sergeant are with the Department Electrical Energy, Systems and Automation, Ghent University, B-9000 Ghent, Belgium
and also with the Department Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, B-9000 Ghent, Belgium (e-mail:
hendrik.vansompel@ugent.be; peter.sergeant@ugent.be).
L. Dupré is with the Faculty of Engineering and Architecture, Ghent University, B-9000 Ghent, Belgium (e-mail: luc.dupre@ugent.be).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2012.2192737
Fig. 1. Considered axial-flux PM machine topology: the YASA or segmented
armature torus topology, which consists of two rotor disks with in between a
stator.
heating of the PM. By increasing temperature, the remanent
flux density of the PM decreases and the magnets may be even
demagnetized irreversibly when the temperature becomes too
high. Luckily in the axial-flux PM machine, cooling of the PM
is achieved by convection in the airgap and by conduction to
the steel rotor. However, before considering thermal modeling
of the machine [2], the local heat sources need to be known as
accurately as possible. In a later step, thermal measurements on
a prototype machine can be used to monitor the temperatures in
the magnets [3], [4].
The axial-flux PM machine considered in this research has the
yokeless and segmented armature (YASA)-topology [5], [6]. As
shown in Fig. 1, the YASA-topology has two rotors on which
the NdFeB PM are placed. Furthermore, the YASA-topology
has a fractional-slot concentrated winding [7]–[9], which generally results in an airgap magnetic field with a high harmonic
content. The main properties of the considered prototype axialflux PM machine, which is a result of the optimization in [10],
are mentioned in Table I.
As the axial-flux PM machine has an inherent 3-D-geometry,
full 3-D-finite-element modeling seems to be necessary in order
to calculate the machine’s properties like cogging-torque and
torque at rated load, phase voltage at no-load and load, [11]
and magnet eddy currents and corresponding losses using transient finite-element analysis [12]–[14]. In [15], the axial-flux
PM machine was considered to be composed of several linear
machines. The overall performance of the axial flux machine
was then obtained by summing the performance of individual
0885-8969/$31.00 © 2012 IEEE
VANSOMPEL et al.: MULTILAYER 2-D–2-D COUPLED MODEL FOR EDDY CURRENT CALCULATION IN THE ROTOR
785
TABLE I
CHARACTERISTICS AND PARAMETERS OF THE AXIAL-FLUX PM
MACHINE-PROTOTYPE
linear machines. This quasi-3-D modeling resulted in a coggingtorque and torque at rated load, phase voltage at no-load and load
that was in good correspondence with the simulations using a
3-D finite-element analysis.
In this paper, the basic idea of the quasi-3-D modeling is
further expanded: the 1-D airgap magnetic fields of multiple
multilayer 2-D finite-element simulations are combined to construct a 2-D airgap magnetic field using static simulations. In a
subsequent step, this 2-D airgap magnetic field is imposed to a
time harmonic 2-D finite-element model of the PM to calculate
the eddy currents and eddy current losses. The limited penetration depth of the time-varying magnetic field in the PM is
hereby taken into account.
In the following sections, first a short discussion about the
airgap magnetic field is done. Second the multilayer 2-D–2-D
coupled model is introduced and in the next section the reference
3-D finite-element model is presented, which is used to verify the
accuracy of the multilayer 2-D–2-D coupled model in Section V.
Fig. 2. No-load airgap magnetic flux density as a function of the rotor position
in the rotor reference frame. Magnetic flux density is evaluated in the center of
the magnet.
the pole pitch. The x indicates that coordinates are expressed
in the stator reference frame, i.e., the coordinate system fixed to
the stator.
As the mageto-motive-force (mmf) of the PM in the rotor
reference frame is given by
∞
π
Fm sin m
x
(2)
f=
Np τ p
m =1
a random mmf-harmonic component with order m
π
x
fm = Fm sin m
Np τ p
(3)
results in the following flux density:
μ0
fm
δ(x)
π
= Bm sin m
x
Np τ p
π
+ Bm sin m
x
Np τ p
∞
n cos nNs Ωt − nNs
bm (x, t) =
II. ANALYSIS OF THE AIRGAP MAGNETIC FIELD
As the eddy currents in the PM are induced by a varying
magnetic field, an analysis of the airgap magnetic field is done
first.
A. Airgap Magnetic Field During No-Load
During no-load operation, a varying magnetic field is exposed
to the PM due to the stator-slotting effect. As the magnet is
passing by a stator slot, the flux density is decreasing locally
due to the higher reluctance. As these stator slots are distributed
equally over the machine’s circumference, a reluctance function
with a periodicity τ , i.e., the slot pitch, can be introduced
∞
1
1
2π =
n cos n x
1+
δ(x )
δkc
τ
n =1
∞
Ns π 1
n cos n
x
1+
.
(1)
=
δkc
Np τ p
n =1
In this equation, δ is the airgap length, kc Carter’s factor, Ns
the number of stator slots, Np the number of pole pairs, and τp
n =1
π
x .
Np τ p
(4)
The first term is related to the magnet mmf-harmonic itself and,
thus, results in a time invariant magnetic flux density, while the
second set of terms, the reluctance harmonics, only consist of
harmonics of order
mδ = nNs n = 1, 2, . . .
(5)
and are responsible for a time-varying magnetic flux density.
Analysis of the magnetic field in a fixed point of the PM as
a function of the rotor position is shown in Fig. 2. In Fig. 3,
the amplitude of the different harmonic components is shown.
As predicted by (5), only harmonics with the order 15, 30, 45,
60, . . . are found.
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Fig. 3. Amplitudes of the different harmonic order present in the airgap magnetic flux density at no-load.
Fig. 4. Airgap magnetic flux density with load as a function of the rotor
position in the rotor reference frame. Magnetic flux density is evaluated in the
center of the magnet.
B. Airgap Magnetic Field With Load
In case that the machine is working at load, an additional
contribution to the varying magnetic flux density related to the
stator armature reaction is added to (4). This contribution is
found by multiplication of a random armature-reaction mmfharmonic component with order m
π
x
(6)
fm = Fm sin Np Ωt − m
Np τ p
with the reluctance function given by (1). After transformation
to the rotor reference frame, the magnetic flux density is given
by (7).
π
x
bm (x, t) = Bm sin (Np + m) Ωt − m
Np τ p
∞
1
n [sin ((Np + m + nNs ) Ωt
2
n =1
π
x
− (m + nNs )
Np τ p
+ sin (Np + m − nNs ) Ωt − (m − nNs )
+ Bm
Fig. 5. Amplitudes of the different harmonic order present in the airgap magnetic flux density at load.
lower than Ns , the subharmonics, and some additional harmonπ
ics that are not a multiple of Ns , the interharmonics.
x .
At the end of this section, it should be remarked that the torque
Np τ p
is generated by the eighth-harmonic component. This harmonic
(7)
component travels in the same direction and at the same speed
The first term consists of harmonic components introduced by as the rotor and thus does not induce eddy currents in the PM.
the armature-reaction mmf. The remaining terms, the reluctance harmonics, represent two series of traveling waves with
III. MULTILAYER 2-D–2-D COUPLED MODEL
harmonic orders
The multilayer 2-D–2-D coupled model consists of three
(8)
mδ = m ± nNs n = 1, 2, . . .
steps, indicated in Fig. 6. In the first step, 1-D flux density
Both terms are traveling with different speeds with respect to the data are calculated using a multilayer 2-D finite-element model
rotor, and thus result in a varying magnetic field with respect to for different rotor positions using static simulations. In the secthe PM. In Figs. 4 and 5, the magnetic flux density as a function ond step, the 1-D flux density data from the different layers are
of the rotor position and the amplitudes of the different harmonic used to build up a 2-D airgap flux density distribution. This rotor
components are shown in a fixed point of the PM. Comparing position dependent data are transformed into the frequency doFig. 3 with Fig. 5, not only harmonic components with orders main, and are used in a third step to calculate the eddy currents in
that are a multiple of Ns are present, but also harmonic orders the PM using 2-D time harmonic finite-element computations.
VANSOMPEL et al.: MULTILAYER 2-D–2-D COUPLED MODEL FOR EDDY CURRENT CALCULATION IN THE ROTOR
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Bn is calculated by
Bn (x, y) = an (x, y) + jbn (x, y)
(10)
where
1
an (x, y) =
π
1
bn (x, y) =
π
Fig. 6. Illustration of the multilayer 2-D–2-D coupled model: (1) multilayer
2-D finite-element model, (2) 1-D flux density data obtained by each of the
multilayer 2-D finite-element models, (3) 2-D time harmonic finite-element
model used for the magnet eddy current calculations.
π
b(x, y, θ) cos(nθ)dθ
(11)
b(x, y, θ) sin(nθ)dθ.
(12)
−π
π
−π
The flux density data Bn can now be used in the time harmonic
eddy current calculations.
C. Time Harmonic Eddy Current Calculation
A. Static Multilayer 2-D Finite-Element Model
In the multilayer 2-D or quasi-3-D finite-element model, the
axial-flux PM machine is considered to be composed of several
linear machines. The overall performance of the axial-flux machine is obtained by summing the performance of the individual
layer machines. Such a linear machine is obtained by defining
a cylindrical surface in the axial-flux PM machine and subsequently unrolling this surface into a 2-D plane. This method
is illustrated in Fig. 7. The number of 2-D computation planes
influences the accuracy of the multilayer 2-D with respect to a
full 3-D model and is related to the geometrical variations in the
radial direction.
For each layer and for each different rotor position, a static
2-D finite-element computation is done by solving the equation
1
∇ × A = Je
(9)
∇×
μ0 μr
where Je is the external current density and the magnetic flux
density is found by B = ∇ × A.
When the solution is found, the 1-D normal component of the
flux density data is stored over one pole pitch.
B. Reconstruction of the 2-D Airgap Magnetic Field
For each rotor position, the normal components of the flux
density data, calculated for the different computation planes, are
brought together. The flux density data are extended by adding
zeros in the zones that exceed the inner- and outer-diameter
limits. This is an approximation with respect to the 3-D finiteelement modeling where fringing fluxes are present at the inner
and outer surfaces. Despite the approximation, the reconstructed
2-D airgap magnetic field obtained by the multilayer 2-D data in
Fig. 8 is in good correspondence with the 2-D airgap magnetic
field calculated using full 3-D finite-element modeling shown
in Fig. 9.
The flux density b, which is a function of the two spatial
coordinates x and y, and the rotor angle θ, should be transformed
to be suitable for the time harmonic eddy current calculation in
the next step. Therefore, for each point in the (x, y)-plane the
amplitude of the nth-order harmonic flux density component
Time harmonic calculation of the magnet eddy current losses
as presented in [16] is used, however, in this paper, the limited
penetration depth of the varying magnetic field in the PM is
taken into account.
Starting from the time harmonic Maxwell equations
∇ × E = −jnΩBn
∇·E=0
(13)
(14)
and the constitutive relation
1
J
σ
the equation to be solved gets the following form
1
∇×
∇ × F = −jnΩBn n = 1, 2, . . .
σ
E=
(15)
(16)
where J = ∇ × F. With respect to magnetic problems, where
a magnetic vector potential A is used, the term electric vector
potential is used to designate F. The Ω in previous equations
indicates the mechanical rotational speed, σ and μ are, respectively, the electrical conductivity and the permeability of the
PM.
For each harmonic component, the finite-element model
(Fig. 10) is using (16) to find the electric vector potential F.
Therefore, the position-dependent flux density values Bn (x, y)
are imposed by spatial interpolation in the flux density data Bn .
Subsequently, this electric vector potential F is used to find the
eddy currents J = ∇ × F.
As these in plane eddy current calculations do not take the
skin effect into account, this should be done afterward. Starting
from the skin depth, which is given by
2
(17)
δn =
nΩμσ
the eddy currents in the magnets are supposed to decrease in
axial direction. This decrease in axial direction is given by
z
Jn = Jn ,0 exp −
.
(18)
δn
where Jn ,0 is the eddy current at the surface of the PM.
Therefore, the magnet eddy current loss of the nth component
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 3, SEPTEMBER 2012
Fig. 7. Principle of the multilayer 2-D or quasi 3-D finite-element model: (1) defining a cylindrical surface in the axial-flux PM machine and (2) subsequently
unrolling this surface into a 2-D plane.
Fig. 8. Airgap magnetic field reconstructed out of the data achieved by the
different static 2-D finite-element computations using second-order elements.
Fig. 9. Airgap magnetic field obtained directly out of the 3-D static finiteelement computations. Due to the numerical limitations, i.e., limited number of
elements and linear elements, the magnetic flux density data shows some numerical noise. Therefore, the 3-D models are coupled using the vector potential
that shows less numerical noice and can be filtered if necessary.
becomes
Ploss,n
1
=
2σ
h m
Jn2 dzdA
A
1
=
2σ
h m
A
magnetic vector potential [17], eddy currents are calculated using time simulations on a 3-D finite-element model that models
a restricted geometry.
0
2z
Jn ,0 exp −
δn
dzdA
(19)
A. Static 3-D Finite-Element Computations
0
where hm is the magnet thickness, i.e., the magnet dimension
perpendicular to the 2-D finite-element computation plane. The
total magnet eddy current is then obtained by summation over
the different harmonic loss components
Ploss =
∞
Ploss,n .
(20)
n =1
IV. REFERENCE 3-D FINITE-ELEMENT MODEL
In order to verify the multilayer 2-D–2-D coupled model, a
3-D finite-element model is introduced in this paragraph as a
reference model. Although this reference model is also a coupled model, the followed approach is fundamentally different
with respect to the multilayer 2-D–2-D coupled model: static
simulations are performed on a 3-D finite-element model, the
coupling between the 3-D-models is done by transfer of the
The static simulations are carried out on a full 3-D finiteelement model. Despite the axial-flux PM machine has the
single-stator-double-rotor topology, only half of the machine
needs to be modeled due to the magnetic symmetry. A overview
of the finite-element model is shown in Fig. 11.
The static simulations are performed for many rotor positions.
After each static simulation, the x-, y-, and z-components of
the vector potential are evaluated and stored in various points
on boundary surfaces that correspond with the boundaries of
the model with the restricted geometry. In these simulations,
the boundary surfaces move with the synchronous speed with
respect to the stator.
The solution for the vector potential is found by solving
∇×
1
∇×A
μ0 μr
= Je
(21)
VANSOMPEL et al.: MULTILAYER 2-D–2-D COUPLED MODEL FOR EDDY CURRENT CALCULATION IN THE ROTOR
Fig. 10. Time harmonic 2-D finite-element model used to calculate the magnet
eddy currents and corresponding losses. (1) Dirichlet boundary condition and
(2) imposition of the processed airgap magnetic field data.
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Fig. 12. Partial 3-D finite-element model used for the time simulations.
(1) Dirichlet boundary condition and (2) imposition of the processed vector
potential data.
B. Vector Potential Data Handling
As the vector potential components are calculated in various
points on boundary surfaces in the rotating reference frame, in
a first step the data are transformed to a stationary reference
frame, i.e., rotor in the 0◦ position. As the coordinates in which
the vector potential components are stored are not uniform distributed, a uniform grid is fitted on the data. Due to numerical
approximation in the 3-D static finite-element simulations, some
numerical noise is found when evaluating one of the components
of the vector potential for different rotor positions at a fixed point
on one of the boundary surfaces. Therefore, the vector potential data are smoothed over the different rotor positions using
a 3-D smoothing spline function. The coefficients of the spline
function are stored, which makes the evaluation of the vector
potential in the time simulations fast.
C. 3-D Finite-Element Time Simulations
Fig. 11. Full 3-D finite-element model used to retrieve the vector potential
data. (1) Dirichlet boundary condition, (2) Neumann boundary condition, and
(3) boundaries on which the vector potential data are recorded.
where
B=∇×A
(22)
and Je is the external current density.
As each static simulation is performed separately, the gauge
function Ψ may be different for each solution and has an impact
on the vector potential by
A = Ã + ∇Ψ.
(23)
As the vector potential data handling includes smoothing over
the different static simulations, the vector potential A should by
unique. Therefore, the Helmholz’s theorem should be fulfilled,
i.e., both ∇ · A and ∇ × A are defined. This is done by setting
the Coulomb gauge ∇ · A = 0.
The 3-D finite-element model with the restricted geometry
in Fig. 12 consists only of one PM and a segment of the rotor.
On the front, left, and right planes of the model, the vector
potential is imposed using the data retrieved from the static full
3-D model. In the 3-D finite-element model with the restricted
geometry, the PM is supposed to be isolated from the steel of
the rotor.
The solution for the vector potential A, is found by solving
the following equation:
1
∂A
+∇×
∇ × A = Je .
(24)
σ
∂t
μ0 μr
V. MODEL COMPARISON AND VERIFICATION
A. Model Calculation Time
The simulations are performed on a Intel(R) Core(TM)2
Quad CPU Q96520 @3.00GHz, with 8.00 GB installed memory
(RAM) running a 64-bit Windows 7 operating system. Finiteelement computations for 2-D as well as 3-D are done using Comsol 3.5a, having the Comsol with MATLAB interface
installed.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 3, SEPTEMBER 2012
TABLE II
CALCULATION TIME REQUIRED FOR EACH PROCESS IN THE MAGNET EDDY
CURRENT LOSS SIMULATIONS
Fig. 14. Magnet eddy current loss at the rated speed of 2500 r/min and rated
load current of 6.67 A as a function of the harmonic order, calculated using the
multilayer 2-D–2-D coupled model.
Fig. 13. Skin depth at the rated speed of 2500 r/min as a function of the
harmonic order.
For the comparison, the multilayer 2-D finite-element model
has six layers with equal layer thickness. The static multilayer
2-D finite-element calculations as well as the 3-D finite-element
computations are done in steps of 0.25◦ rotor position. During
the data handling, both calculation methods are reconstructing
the airgap magnetic field in uniform grid having a resolution
of 1.0 mm. For the calculation of the losses, in the multilayer
2-D–2-D coupled model takes only the first 150 harmonic components into account. In the reference 3-D finite-element model
three full rotations of the rotor discs are necessary to obtain the
steady-state solution.
The data necessary for the calculations of each individual
process are mentioned in Table II. Notice that in case of the
multilayer 2-D finite-element model, six 2-D finite-element
calculations are required for each rotor position. The data in
Table II show a massive reduction in calculation time, which
was the main target of the introduction of the multilayer 2-D–
2-D coupled model.
B. Model Accuracy
As the magnet eddy currents losses are calculated in two
very different ways, verification of the accuracy can only be
done using the final result, i.e., the time average of the magnet
eddy current losses. For the multilayer 2-D–2-D coupled model,
this is done by taking the sum of the average power loss of
each harmonic component, which is mathematically expressed
in (20). In Figs. 13 and 14, for each harmonic order the skin
depth and corresponding average power loss are presented. As
could be expected based on the harmonic content of the airgap
magnetic field in Fig. 5, the multiples of 15 represent the highest
power losses.
Fig. 15. Instantaneous magnet eddy current losses as a function of the rotor
position at the rated speed of 2500 r/min and rated load-current of 6.67 A,
calculated using the reference 3-D finite-element model.
For the reference 3-D finite-element model, the magnet eddy
current loss is found by taking the time average of the instantaneous power loss. The instantaneous eddy current loss is shown
in Fig. 15 as a function of the rotor position. Again, the dependence of the magnet eddy current losses and the slot number is
clear.
Comparing both time average values of the magnet eddy
current losses, 0.2655 and 0.2679 W per magnet are found for the
multilayer 2-D–2-D coupled model and reference 3-D model,
respectively. So despite the very different calculation methods,
less than 2% difference in the calculated magnet eddy current
losses is found.
Another parameter that can be easily compared is the airgap
magnetic field. In Fig. 8, the airgap magnetic field obtained
by the magnetic field reconstruction using the multilayer 2-D
finite-element data is shown, which is in very good correspondence to the airgap magnetic field (see Fig. 9) that is directly
obtained by the static 3-D finite-element computations. More
VANSOMPEL et al.: MULTILAYER 2-D–2-D COUPLED MODEL FOR EDDY CURRENT CALCULATION IN THE ROTOR
complex magnet shapes will require more layers in the multilayer 2-D finite-element model to obtain a sufficient accurate
airgap magnetic field; however, as these 2-D simulations are
very fast this will have only a minor influence on the calculation
time.
VI. CONCLUSION
In this paper, a multilayer 2-D–2-D coupled model was introduced to calculate the magnet eddy current losses in axial-flux
PM machines. In this model, the 3-D geometry of the axial-flux
PM machine is considered to be composed of several linear machines. The 1-D airgap magnetic field of each individual layer is
used to reconstruct the 2-D airgap magnetic field. This magnetic
field is imposed to a time harmonic 2-D finite-element model to
calculate the eddy currents and and its corresponding losses. As
this modeling technique requires only 2-D finite-element computations, the simulation time can be strongly decreased with
respect to magnet eddy current calculation based on 3-D finiteelement computations. Simulations using 3-D finite-element
modeling were used to prove the accuracy of the introduced
model: reconstruction of the airgap magnetic field as well as the
calculation of the magnet eddy current losses show very good
correspondence.
[13] K. Yamazaki, Y. Fukushima, and M. Sato, “Loss analysis of permanentmagnet motors with concentrated windings-variation of magnet eddycurrent loss due to stator and rotor shapes,” IEEE Trans. Ind. Appl.,
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Eddy-current loss in permanent-magnet brushless AC machines,” IEEE
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[16] J. D. Ede, K. Atallah, G. W. Jewell, J. B. Wang, and D. Howe, “Effect
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Hendrik Vansompel was born in Belgium in 1986.
He received the Bachelor and Master degrees in
electromechanical engineering from Ghent University, Ghent, Belgium, in 2008 and 2009, respectively,
where he is currently working toward the Ph.D. degree in the Department of Electrical Energy, Systems
and Automation.
His current research interests include electrical
machines modeling and design, particularly for sustainable energy systems.
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Peter Sergeant received the M.S. and Ph.D. degrees
in electromechanical engineering from Ghent University, Ghent, Belgium, in 2001 and 2006, respectively.
He has been a Postdoctoral Researcher for the
Fund of Scientific Research Flanders since 2006, and
a Researcher in the University College Ghent, Ghent,
since 2008. His current research interests include numerical methods in combination with optimization
techniques to design nonlinear electromagnetic systems, in particular, electromagnetic actuators.
Luc Dupré was born in 1966. He received the Graduate degree in electrical and mechanical engineering
in 1989 and received the Doctorate degree in applied
sciences in 1995, both from the University of Gent,
Ghent, Belgium.
He is currently a Full Professor in the Faculty
of Engineering and Architecture of Ghent University. His research interests mainly include numerical methods for electromagnetics, modeling, and
characterization of soft magnetic materials, micromagnetism, inverse problems, and optimization in
(bio)electromagnetism.