Analysis of Different PM Machines with
Concentrated Windings and Flux Barriers in
Stator Core
Gurakuq Dajaku, Dieter Gerling
Abstract - The new stator structure with magnetic flux-barriers
in the stator yoke or tooth region represents an efficient method
for reducing the sub-harmonics of electric machines with
fractional slots, tooth-concentrated windings. In this paper the
both flux-barriers techniques are considered during the analysis
of different PM machines. The 12-teeth single-layer and
double-layer concentrated winding in combination with a
10-poles and 14-poles PM rotor are investigated. For the all
machine topologies the new stator design is used to improve their
performances and characteristics. The flux-barrier effects on the
main machine parameters, such as in the air-gap flux density
harmonics, dq-machine parameters, characteristic currents,
electromagnetic torque, and so on, are studied carefully.
Comparisons performed with the analogous conventional
machines (with conventional stator) show that, the new stator
design offers significant advantages.
Φ
Index Terms— Tooth concentrated winding, MMF harmonics,
magnetic flux-barrier, permanent magnet synchronous machines,
finite elements method.
I. INTRODUCTION
RACTIONAL slot tooth concentrated windings (FSCW)
are widely using by permanent magnet (PM) synchronous
machines. Especially for the applications where the available
space and packaging is limited, at the moment this winding
type appears to be a single solution. Recently, the FSCW are
usually used by PM machines, however the interest on this
winding type are growing up also for others electric machine
types such as synchronous reluctance machines [1, 2] and
asynchronous machines [3, 4]. The use of concentrated
windings offers several advantages which are discussed and
studied widely in many literatures [5-7], however they are
related also with some drawbacks such as the high losses in
rotor (iron core and permanent magnets) [8 to 10], and the
noise and vibration effects [11 to 13]. It is important to point
out that these negative effects results mostly from the nonsinusoidal distribution of the magneto motive force (MMF)
distribution produced from the stator winding. With other
words, the magnetic field of these windings has more space
harmonics, including sub-harmonics. For the PM machines,
the torque is developed by the interaction of a specific high
stator space harmonic with the corresponding number of
F
G. Dajaku is Senior Scientist with FEAAM GmbH, D-85577 Neubiberg,
Germany (e-mail: Gurakuq.Dajaku@unibw.de).
D. Gerling is Full Professor at the University of Federal Defense Munich,
Institute for Electrical Drives, D-85577 Neubiberg, Germany (e-mail:
Dieter.Gerling@unibw.de).
978-1-4799-4775-1/14/$31.00 ©2014 IEEE
permanent magnet poles in rotor, however, the rest of others
sub- and high harmonics, which rotate with the different speed
and also in opposite directions, lead to undesirable effects in
the machine. Analogous, also for the asynchronous machines,
the winding harmonics induce additional rotor currents and
opposing torques with limited net torque and high rotor bar
losses compared to a conventional distributed winding.
Therefore, to improve the MMF winding performances of
the FSCW regarding to power losses and noise problems
several methods and techniques are developed and
investigated in the past [14 to 23]. Generally, according to
these methods, the air-gap flux density harmonics produced
from the winding MMF can be reduced or completely
suppressed by modifying the winding layout [14, 21] or using
magnetic flux barriers in some specific stator core locations
[22, 23]. The investigations carried out through these works
show that using different optimizations techniques brings
enormous improvements on the PM machine performances
such as reduction of the sub- and high MMF harmonics more
than 60%, reduction of radial force modes of low order,
reduction of the machine losses (magnet losses, iron losses
and so on), improves the cooling capability (direct cooling of
coil windings), reduce the slot proximity effects, and so on.
In this paper, the new stator structure with magnetic
flux-barriers in stator core region (yoke and teeth) is
considered during the analysis of different PM machines with
concentrated windings. The widely used 12-teeth single-layer
(SL) and double-layer (DL) windings are taken as exemplary
windings for different 10-poles and 14-poles machine designs.
The main objective of this work was to investigate the
flux-barrier effect on their main machine parameters such as
the electromagnetic torque, inductances, flux-linkage, and also
on the field weakening capability. The design and analysis of
the studied machines is performed using 2D finite elements
method (FEM). For the all exemplary machines, several
steady state and in time-domain simulations are performed and
also different load conditions are investigated, and finally the
obtained results are compared with the analogous conventional
stator designs.
II. THE 12-TEETH TOOTH CONCENTRATED WINDING
Using FSCW, there are many possible slot number and pole
number combinations for PM machines. The stator coils may
be wound either on all the teeth (double layer winding, DL) or
only on alternate teeth (single-layer winding, SL). Fig. 1
shows different concentrated winding layouts wound in a
12-teeth stator core. SL winding have coils wound only on
alternate teeth, whereas each tooth of the DL windings carries
375
a coil. The winding layout and the winding factor of a PM
machine with concentrated winding depend on its combination
of pole and slot number. Therefore, this combination should
be chosen carefully in order to maximize the fundamental
(MMF working harmonic) winding factor and thus the torque
density. SL windings are preferred to DL windings when a
high fundamental winding factor and high fault-tolerance is
required. Otherwise, DL windings are preferable to limit the
losses and torque ripple.
A. Winding Function Analysis
The MMF distribution for one-phase of considered windings
are illustrated in the following Fig. 2. Using Fourier series
function the MMF distribution can be described using the
following eqs. (1) and (2).
ν
ν =1,3,5,...
πν
⋅ i ⋅ cos ( νφS )
⎛ π⎞
ξ w ,SL = sin ⎜ ν ⎟
⎝ 12 ⎠
Θ DL (φS , t) =
ν
4 ⋅ N w1 ⋅ ξ w ,SL
∑
ξ w ,DL
8 ⋅ N w 2 ⋅ ν ξ w ,DL
ν =1,3,5,...
πν
⋅ i ⋅ cos ( νφS )
⎛ 5π ⎞
⎛ π⎞
= cos ⎜ ν ⎟ ⋅ sin ⎜ ν ⎟
⎝ 12 ⎠
⎝ 12 ⎠
π
(2)
π/6
where, with ν ξ w is denoted the winding factor, i is the phase
current, ω is the angular frequency, Nw is the number of turns
per coil, and ν are the MMF winding harmonic. The indexes
SL and DL are used for the single-layer and double-layer
winding, respectively.
Fig. 3 compares the harmonic contents of the considered
FSCW types, however, Table-I show the winding factors for
the first three harmonics in the MMF spectrum. As can be
seen here, the main difference between the presented winding
types is not only in the winding layout, but also on the MMF
spectrum. For the SL winding, the winding factors for the 5th,
7th (possible working harmonics) are for about 3.3% higher
compared with the DL winding, that means, regarding to the
torque density the SL winding overcome the analogous DL
winding. However, the 1st MMF sub-harmonic for the SL
winding is relatively too high which induce huge losses in the
rotor core and magnets [8-10] and thus it decreases the torque
density and the efficiency of the machine. Therefore, as results
of high rotor losses, the PM machines with the DL winding
are mostly used in many applications.
TABLE-I: Winding factors
ν
ξw
Nw ⋅ i
(1)
x
∞
∑
b)
Θ(x)
st
th
th
SL
1
25.8%
5
96.6%
7
96.6%
DL
6.7%
93.3%
93.3%
Θ(x)
Nw ⋅ i
x
π
π/6
Fig. 2: MMF distribution of one phase, a). SL winding, b). DLwinding.
1.4
Single-Layer
Double-Layer
1.2
5th or 7th =>working harmonics
1
MMF [ p.u. ]
ΘSL (φS , t) =
ν
∞
a)
Fig. 1: Available winding layouts for the 12-teeth FSCW, a). SL winding,
b). DL winding.
0.8
0.6
0.4
0.2
0
1
3
5
7
9
11
13
Space Harmonics
15
17
19
Fig. 3: MMF winding harmonics for the 12-teeth SL and DL FSCW.
376
B.
Reduction of sub-harmonics using flux-barriers in stator
core region
Let’s remind here that, except the well know conventional
FSCW with q=0.5 (+A,+B,+C), the rest of others concentrated
windings use the high MMF harmonics as working harmonic.
This is shown also from the previous Table-I and Fig. 3, where
the high harmonics, such as the 5th and the 7th, have the
highest winding factors. On the other side, the harmonics of
low orders such as the 1st one rotate with different speed
referred to the fundamental harmonic, and due to the large
wave length they flow deeply inside the rotor region and
induce there large rotor losses in the iron core and also in
magnets. Therefore, to reduce the effects of sub-harmonics in
PM machines with FSCWs, references [22 and 23] show two
new stator structures with magnetic flux barriers in specific
stator core locations which are illustrated in Fig. 4. For the
12-teeth/10-poles PM machine the new stator structure with
flux barriers in the yoke regions beside every second stator
slot present an efficiency solution for the both winding
layouts. However, another alternative solution using flux
barriers on the teeth region (every second teeth) is also an
efficient and promising technique for the 12-teeth/14-poles
PM machine with the SL winding.
110
BvFB / BvConv [ % ]
100
a)
90
v=1
v=5
v=7
80
70
60
50
40
0
20
40
hB / hY
60
80
100
[%]
Fig. 4 show the flux barrier effect on the air-gap flux
density due to reaction field of different PM machines with SL
and DL winding. The simulations results are obtained using
finite elements method (FEM). The all machine types are
investigated under the same load condition (Ieff = 35A), and
the results are presented as a relative ratio of the air-gap flux
densities components of the new machine design to the
corresponding conventional machine with the conventional
stator. As before, only the first three air-gap flux density
harmonics are investigated ( Bν , FB / Bν ,Conv where, v = 1, 5, and
7).
As well is shown from Fig. 4a), for the electric machine
with the SL winding the 1st sub-harmonics decrease linearly
with increasing of the flux-barrier depth parameter hB. It can
be concluded here that a completely cut out of the yoke region
st
reduces the 1 sub-harmonic about 60%. On the other side, the
th
th
other harmonics such the 5 and the 7 are positively
influenced (slightly increased). Analogous, also for the electric
machine with the DL winding, the flux-barriers in stator yoke
region reduce the air-gap flux density sub-harmonics. Fig. 4b)
st
shows that for this machine type the 1 sub-harmonic
completely can be suppressed by choosing a proper
flux-barrier depth (hB equal to 65% of hY.). However, contrary
to the SL design, here the flux-barriers slightly reduce the 5th
and the 7th high harmonics. Further, also the results presented
in Fig. 4c) for the new stator design with flux-barriers in the
teeth region show significant improvements in the air-gap flux
density harmonics. For the SL winding type, the flux-barriers
st
th
decrease significantly the 1 and the 5 harmonics, but
simultaneously increase the amplitude of the air-gap flux
th
density for the 7 harmonic. Therefore, as result of the positive
th
effect on the 7 harmonics, the new stator structure is suitable
for a 14-poles machine with the SL winding.
III. ANALYSIS OF DIFFERENT PM MACHINES
120
BvFB / BvConv [ % ]
100
b)
80
60
40
v=1
v=5
v=7
20
0
0
20
40
hB / hY
60
80
100
40
50
[%]
120
BvFB / BvConv [ % ]
100
TW
c)
FB
80
60
40
20
0
0
v=1
v=5
v=7
10
20
FB / TW
30
[%]
Fig. 4: Flux-barrier effect on the air-gap flux density harmonics;
a). 12-teeth/10-poles SL winding, b). 12-teeth/10-poles DL winding,
c). 12-teeth/14-poles SL winding.
During the following work several PM machines with SL
and DL winding topology and magnetic flux-barriers in the
stator yoke/teeth regions are investigated. For each machine
topology illustrated in Fig. 4, also the analogous PM designs
with the conventional stator core are considered as
corresponding reference machines. In total there are six PM
machines that are analyzed and compared. The main geometry
data of the studied PM machines are resumed in Table-II. The
flux barrier depth for the 12-teeth/10-poles SL and DL design
are taken to be 0.95 * h Y and 0.65 * h Y, respectively, however the
flux barrier width for the 12-teeth/14-poles design is taken to
be 0.33 * TW. For the all machine designs the electrical and
geometrical constrains are taken to be the same (UDC = 12 V,
Ieff = 35Arms and volume: DOut=81mm, LStack=70mm). Further,
the same stator and rotor design, the same number of turns per
phase and also the same magnet material amount is considered
for the all examples; the only difference on the investigated
machine geometries is the stator core (with- and without flux
barriers) and the winding layout (single-/ double-layer).
The simulation results presented in the following are
performed using finite elements (FE) method. Analogous to
the previous section, the same load condition (35Arms load
current) is considered. Further, for each machine topology, the
377
main machine parameters such as, the electromagnetic torque
and torque ripple, inductances, flux-linkages, characteristic
currents, and so on are determined and compared with the
corresponding reference designs.
a)
Conv.
Design
New
Stator
b)
Conv.
Design
New
Stator
c)
New
Stator
Conv.
Design
Fig. 5: Flux-density distribution due to reaction field (Ieff=35A);
a). 12-teeth/10-poles SL winding, IPM-1, b). 12-teeth/10-poles DL winding,
IPM-2, c). 12-teeth/14-poles SL winding, IPM-3.
Table-II: Main geometry parameters
IPM-1
IPM-2
IPM-3
Outer stator diameter
[mm]
81
81
81
Outer rotor diameter
[mm]
48
48
48
Gap length
[mm]
0.5
0.5
0.5
Magnet length
[mm]
3
3
3
Magnet width
[mm]
10
10
7.12
Active length
[mm]
70
70
70
Turns per coil
[--]
20
10
20
Parallel path
[--]
2
2
2
Number of stator teeth
[--]
12
12
12
Number of rotor poles
[--]
10
10
14
SL
DL
SL
Winding Type
A. Flux density due to reaction field
The flux-barrier effect on the air-gap flux density
harmonics due to reaction field is already investigated in the
previous section. According to the obtained results it can be
concluded that for the all machine types the new stator
structure reduce efficiency the sub-harmonics. The field lines
distribution under the given load condition are presented in
Fig. 5. Considering firstly the PM machine design with SL
winding and also with conventional stator, at the first sight,
the flux distributions it seems to be analogous with a two poles
machine. This is as results of the high 1st sub-harmonic
component generated from this winding type. However, using
the new stator core with flux-barriers in stator yoke or teeth
region, they limit the first component of the flux density to
flows around one-half of the machine, and with this the
sub-harmonic component is suppressed. Therefore, the flux
distribution for the considered machines with SL winding and
also the new stator structure is analogous with the DL machine
design and conventional stator. On the other side, for the DL
winding design, the flux-barriers reduce completely the
sub-harmonic components, and according to Fig. 5b), the flux
lines distribution with the new stator are more uniformly
distributed around the air-gap.
As is mentioned previously, the FSCW produce several
harmonic components in the air-gap flux density of the PM
machines. Except the fundamental or working harmonic
component, the other harmonics rotate with different speed
and also in different direction compared with the rotor
synchronous speed. Therefore, due to the asynchronous effect
of these harmonics, the resulting flux density components
induced in the rotor fluctuate with the time. In the rotor
reference frame these harmonics can be described using the
following relation [24],
ˆ sin ( k ⋅ ωt ± ν ⋅ θ + α ) , k = − ν ± 1
(3)
B(t, θ) = ∑ ∑ B
ν ,k
ν ,k
p
ν
k
where, k is the order of the time harmonics generated from the
v MMF space harmonic, B̂ν ,k is the time kth order and the vth
spatial order magnetic flux density. “+” and “-“ denotes the
positive, respectively the negative going wave.
In order to show the flux-barrier effects on the flux density
components induced in the rotor, below, the all exemplary
machines are investigated in time domain. Under the same
load current, the simulations are carried out for one
mechanical rotor rotation and the flux density on the magnet
surface (as is illustrated in Fig. 6) is observed with the time.
Investigation point for
the rotor flux density, B(t, θ)
Fig. 6: Rotor investigation location during the time domain analysis.
378
Figs. 7(a) to 7(c) show the flux density results on the specified
magnet location. The FFT analysis is applied to determine the
time harmonics in the flux density curves. As well is shown
here, the main time flux density harmonics induced in the
rotor are the 6th, 12th, 18th, and 24th. From eq. (3), the 6th time
harmonic is induced from the 1st space harmonic, the 12th time
harmonic is induced from the 7th and the 17th, and the 24th time
harmonic is induced from the 19th space harmonic. It is
B [T]
0.5
Conv. Stator
New Stator
0
-0.5
0
100
200
position [mech. degree]
B [T]
a)
Conv. Stator
New Stator
0.1
0.05
0
5
10
15
20
Order of time harmonics
B [T]
0.5
100
200
position [mech. degree]
B [T]
C. Machine parameters
The machine parameters plays a key role for determining
various aspects of the PM machine characteristics, such as, the
flux-weakening capability, torque components, fault currents
and so on. The analysis of a PM machine is conveniently
carried out in a d-q rotating reference frame. The steady-state
equations for the voltage and the electromagnetic torque are,
ud = R ⋅ id − ω Lq ⋅ iq − ωψ qm
300
0.05
5
10
15
20
Order of time harmonics
0.5
25
30
Conv. Stator
New Stator
0
-0.5
0
100
200
position [mech. degree]
c)
300
Conv. Stator
New Stator
0.1
Te =
3
p ⎡( Ld − Lq ) ⋅ id ⋅ iq + (ψ dm ⋅ iq −ψ qm ⋅ id ) ⎤⎦
2 ⎣
Table-III: Electromagnetic torque and torque ripples of considered machines
IPM-1
T_av
5
10
15
20
Order of time harmonics
25
(5)
where ψ m is the flux-linkage due to the permanent magnets, L
is the machine inductance, and Te is the electromagnetic
torque. Further, the dq-indexes represent the d- and q- axis
components of the machine parameters.
In order to examine the influence of the magnetic
flux-barriers on the machine parameters, the FE investigations
performed in following are carried under the same load current
as before, but additionally for different current load angles.
Furthermore, the saturation and also the cross-coupling effects
are considered during determination of the machine
parameters with the fixed permeability FE method [25, 26].
The obtained results for different load conditions are presented
in Figs. 9 and 10.
0.05
0
(4)
uq = R ⋅ iq + ω Ld ⋅ id + ωψ dm
Conv. Stator
New Stator
0.1
0
B. Electromagnetic Torque
During determination of the electromagnetic torque the
simulations are performed for different rotor positions and for
the same load condition as before. The torque behavior vs.
rotor positions (one electrical period) are presented and
compared in the following Fig. 8. Additionally, the values for
the average torque and torque ripples are resumed in Table-III.
Analyzing the obtained results it can be concluded that for the
10-poles PM machine designs (IPM-1 and IPM-2) the
flux-barrier effect represents only minor effect in the torque
components, however, for the 14-poles PM machine with SL
winding (IPM-3) the new stator structure increase the torque
density for about 15%. Also the torque ripples are improved
for this machine design.
30
0
b)
B [T]
25
Conv. Stator
New Stator
-0.5
0
B [T]
300
important to point out that these time harmonics are mainly
responsible for the rotor losses (iron core and magnets).
Therefore, using the new stator design with magnetic
flux-barriers, these harmonics significantly are reduced which
leads to the rotor loss reduction [22, 23].
[Nm]
30
T_rippl
Fig. 7: Results of time analysis for the rotor flux density due to the reaction
field; a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
379
[%]
IPM-2
IPM-3
Conv. Stator
3.97
4.15
3.87
New Stator
4.12
4.05
4.55
Conv. Stator
11.2
10
12.25
New Stator
10.4
9.87
9.98
5
0.3
0.25
3
0.2
Conv. Stator
New Stator
2
a)
L [ mH ]
a)
T [Nm]
4
0.15
0.1
1
Ld_conv
Lq_FB
Lq_conv
Ld_FB
0.05
0
0
60
120
180
240
300
rotor position [el. degree]
0
360
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
5
0.3
0.25
3
0.2
Conv.…
New Stator
2
b)
1
L [ mH ]
b)
T [Nm]
4
0.15
0.1
Ld_conv
Lq_FB
Lq_conv
Ld_FB
0.05
0
0
60
120
180
240
300
rotor position [el. degree]
0
360
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
80
90
5
0.3
0.25
3
0.2
Conv.…
c)
2
1
L [ mH ]
c)
T [Nm]
4
0.15
0.1
Ld_conv
Lq_FB
Lq_conv
Ld_FB
0.05
0
0
60
120
180
240
300
rotor position [el. degree]
0
360
0
ν
ν
20
30
40
50
60
70
Fig. 9: dq-inductances vs. current load angle for Ieff =35A;
a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
The simulation results show that, the winding inductances
for the SL and DL winding are different even the number of
turns per phase is taken to be the same (see Table-II). This
property can be explained by analyzing their winding
inductance functions. Relation (6) describe the inductance
function derived according to [27, 28] which includes the
synchronous plus harmonic inductance. With L1 and L2 are
denoted the winding inductances for the SL and DL winding.
16
1
L1 = N 2w1 ⋅ r ⋅ l ⋅ Λ 0 ⋅ ∑ ν ξ w21
π
ν ν
(6)
16
1ν 2
2
L2 = 2 N w 2 ⋅ r ⋅ l ⋅ Λ 0 ⋅ ∑ ξ w 2
π
10
Load angle [el. degree]
Fig. 8: Electromagnetic torque vs. rotor position;
a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
In the above eq. (6), with r is denoted the air-gap radius, l is
the machine effective length, and Λ0 is the magnetic
permeance.
From (6), the ratio between synchronous inductances for the
SL and DL winding is
2
2
L1 1 ⎛ N w1 5ξ w1 ⎞
1 ⎛ 20 0.966 ⎞
= ⎜
⋅
⎟ = ⎜ ⋅
⎟ = 2.1
L2 2 ⎝ N w 2 5ξ w 2 ⎠
2 ⎝ 10 0.933 ⎠
(7)
Eq. (7) indicates that the SL winding has higher inductance
compared with the analogous DL winding. In the FE results
presented in Fig. 9, it is shown that for the conventional stator
case the ratio between these inductances, depending on the
380
In above eq. (8) with n Θˆ PM the amplitude of the rotor MMF
due to magnets, and n are the rotor MMF space harmonics.
14
12
Flux [ mVs ]
10
a)
8
Flux-Q, conv.
Flux-Q, FB
Flux-D, conv.
Flux-D, FB
6
4
2
0
-2
-4
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
14
12
b)
Flux [ mVs ]
10
8
Flux-Q, conv.
Flux-Q, FB
Flux-D, conv.
Flux-D, FB
6
4
2
0
-2
-4
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
80
90
10
8
c)
Flux [ mVs ]
load condition, is between 1.5 and 1.6, and compared with
relation (7) the inductance ratio is lower. The main reason for
this discrepancy is on that, the relation (7) consider only the
synchronous inductance, however if the slot-leakage
inductance and also the saturation effect are considered, then
the deviation between the FEM and the analytical models
would be closer. On the other side, comparing the inductance
results for the conventional- and also the new stator design, it
can be seen that, for the SL winding the flux-barriers have a
considerable effect on the dq-inductance results. For this
winding type the flux-barriers reduce the coupling effect
between the phase coils (opposite coils of one-phase) and also
the 1st sub-harmonic which are the main factors that leads to
the inductance reduction. Otherwise, for the DL winding
design, the flux-barriers effect on the dq-inductances is
minimal, even in the flux density we can see a more uniformly
distribution of the flux lines around the air-gap than for the
conventional stator. In contrast to the SL winding, the relative
amount of the 1st sub-harmonic in the winding inductances is
clearly small, and therefore the reduction of this harmonic has
a negligible effect on the machine inductances.
Further FE simulation results for the flux-linkages due to
PM for different load conditions are given in Fig. 10. In these
diagrams the two components of the flux-linkages are
presented. As well is known, the d-axis component is the main
PM flux-linkage component, however the q-axis component is
a parasitic component which appears as results of the cross
coupling effect when the saturation in the machine occurs.
This can be seen also from the flux-linkage results for the SL
winding where, due to high component of sub-harmonics the
saturation in the machine is higher compared with the DL
machine design, and with this also the q-axis flux-linkage
component is higher. It is important to remember here that this
parasitic component influence negatively the electromagnetic
torque (please see eq. (5)). Therefore, the reduction of this
component using the new stator design is an additional
advantages regarding to the torque capability of the machine.
On the other side, considering again the SL design, the fluxbarriers in the stator yoke region decrease the d-axis
flux-linkage component for the 10-poles machine design
(IPM-1), however, in contrast for the 14-poles machine
(IPM-3) the new stator with flux-barriers in the stator teeth
region increase the main components of the PM flux-linkage.
As results, the torque density of this machine type additionally
is improved. Further, comparing the flux-linkage results for
the conventional stator, it can be seen that there exists a small
difference between the SL and the DL design even the number
of turns per phase and also the amount of the magnet material
in rotor is taken to be the same. This can be validated also
with the flux-linkage functions presented in (8) and (9).
4
1n
ˆ
ψ 1 = N w1 ⋅ r ⋅ l ⋅ Λ 0 ⋅ ∑
ξ w1 ⋅ n Θ
PM
p
n
n = p (1,3,5,..)
(8)
4
1n
n ˆ
ψ 2 = 2 N w2 ⋅ r ⋅ l ⋅ Λ0 ⋅ ∑
ξ w2 ⋅ Θ PM
p
n = p (1,3,5,...) n
6
FluxQ, conv.
Flux-Q, FB
4
2
0
-2
-4
0
10
20
30
40
50
60
70
Load angle [el. degree]
Fig. 10: dq-PM flux-linkage vs. current load angle for Ieff =35A;
a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
From (8), the ratio between the flux-linkage components for
the SL and DL winding is
5
ψ1
N
ξ
20 0.966
= w1 ⋅ 5 w1 =
⋅
= 1.036
ψ 2 2 N w2 ξ w1 2 ⋅10 0.933
(9)
D. Field weakening characteristics
The field weakening capability of PM machines depends
on the machine parameters and particularly from the winding
inductances. Generally, PM machines with concetrated
windings are characterized with high winding inductance and
thus with high flux weakening capability. According to [29],
the characteristic current Ich is the best indicator for the
381
flux-weakening capability of PM machines, which is defined
as follows
60
(10)
Fig. 11 show the characterisitcs currents for the considered
machines with and without flux-barriers in stator. The
machine parameters given in previous section are used in (10)
for determination of Ich. From the results it can be seen that the
SL winding design is characterized with low characteristic
curent compared with the DL winding. This is as results of
high winding inductance for this winding type. Additionally,
for the SL winding type the flux-barriers increase the
characteristic current up to 32%, however, for the double
winding his effect is negligible. Therefore, at the first point of
view, regarding to the field weakening capability the SL
winding design show to be a good solution compared with the
DL winding, and unfortunately the new stator design decrease
this capability. However, this conclusion isn’t always true
because the field weakening capability depend on many
parameters such as load current, saturation condition and so
on. To have a clear answer regarding to this feature, in Fig. 12
the torque-speed characteristics of the considered machines
are investigated for different load currents. The simulations
are performed according to the previous relations (4) and (5)
and under the fixed 12V DC voltage condition. Based on these
results, the field weakening capability of the machines is
different depending on the load currents. For the IPM-1 design
with the SL winding the flux barriers improves the
torque-speed characteristics at high load current, however, at
low current they show an contrary effect. Further, the DL
machine design at high load show analogous performances as
the IPM-1 with flux barriers, and the new stator design doesn’t
influence its torque-speed characteristics. However, at lower
load, as results of low inductance the field weakening
characteristics of this machine type are degraded. And finally
for the IPM-3 design, the new stator shows a positive effect
for the both load currents. Therefore, considering these results
it can be concluded here that only a high d-axis inductances is
not always responsible for a good field weakening capability,
however, according to voltage equations given in (4) the both
Ld and Lq inductance parameters are responsible for the
maximal voltage and field weakening characteristics of the
machine. As results of a high Lq inductance for the
conventional stator design the ud voltage increase rapidly with
the rotor speed, and the sum of voltage components ( uq2 + ud2 )
reach early the voltage limit and also the field weakening
region. On the other side, for a specific load current, the high
Ld inductance sometimes can produce an over weakening of
the magnet flux that results to a linearly increase of the uq
voltage with the speed in the negative region.
IV. CONCLUSION
The new stator design with magnetic flux-barrier in stator
yoke or in tooth region is an efficiency method for reducing
the air-gap flux density sub-harmonics of PM machines with
FSCW. Using this new technique, the resulting additional
rotor losses (permanent magnets and rotor core), and also the
a)
Psi_pm / Ld
[Arms]
40
20
0
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
80
Conv. Stator
New Stator
60
b)
Psi_pm / Ld
Ld
Conv. Stator
New Stator
40
20
0
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
80
Conv. Stator
New Stator
Psi_pm / Ld
I ch =
ψ dm
80
60
40
20
0
0
10
20
30
40
50
60
70
Load angle [el. degree]
80
90
Fig. 11: Characteristic current vs. current load angle for Ieff =35A;
a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
other parasitic effect can be reduced or completely canceled.
On the other side, also the other machine parameters and
performances are influenced with the new stator structure. To
show that, different PM machines with different pole/slot
combinations, and also with the conventional and the new
stator structure are consider during this work. The all
exemplary machines are designed under the same electrical
and geometrical constrains, and the only difference is taken to
be in the stator design (conventional and the new stator with
flux-barriers). The main machine parameters and
performances, such as air-gap flux density characteristics, dqparameters, characteristic currents, electromagnetic torque,
and the field weakening capability are investigated carefully
382
REFERENCES
8
T [Nm]
6
a)
[1]
New Stator, 60A
Conv. Stator, 60A
New Stator, 35A
Conv. Stator, 35A
[2]
4
[3]
2
[4]
0
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400
8
T [Nm]
speed [ rpm ]
[5]
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Conv. Stator, 60A
New Stator, 35A
Conv. Stator, 35A
6
b)
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[7]
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[8]
0
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6
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[12]
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[13]
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[14]
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a). IPM-1 machines, b). IPM-2 machines, c). IPM-3 machines.
[15]
and are compared with the analogous conventional machine
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new stator design brings several advantages over the
conventional design such as:
ƒ Sub-harmonic reduction more than 60%. The resulting
rotor losses significantly can be reduced.
ƒ Torque density improvements. Especially, for the
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technique shows torque increase up to 16%.
ƒ High field weakening capability. The flux-barriers
reduce the winding harmonic inductances. For the SL
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V. BIOGRAPHIES
Gurakuq Dajaku was born in 1974 in Skenderaj, Kosova. He received the
diploma degree in electrical engineering from the University of Prishtina,
Kosova, in 1997 and the Ph.D. degree from the Universitaet der Bundeswehr
Muenchen, Munich, Germany, in 2006. Since 2007 he has been a Senior
Scientist with FEAAM GmbH, an engineering company in the field of electric
drives. Since 2008 and 2010 he has been a Lecturer at the Universitaet der
Bundeswehr Muenchen, Germany, and the University of Prishtina, Kosova,
respectively. His research interest is in the field of electrical machines and
drives. He has published numerous technical papers in different IEEE journals
and conferences and has several international patents and patent pending
applications. Dr. Dajaku received the Rheinmetall Foundation Award 2006
and the ITIS (Institute for Technical Intelligent Systems) Research Award
2006.
Dieter Gerling was born in 1961 in Menden/Sauerland, Germany. He
received the diploma and Ph.D. degrees in electrical engineering from the
Technical University of Aachen, Aachen, Germany, in 1986 and 1992,
respectively. From 1986 to 1999, he was with Philips Research Laboratories,
Aachen, as Research Scientist and later as Senior Scientist. In 1999, he joined
Robert Bosch GmbH, Bühl, Germany, as Director. Since 2001, he has been a
Full Professor at the Universitaet der Bundeswehr Muenchen, Munich,
Germany (http://www.unibw.de/EAA/).
384
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