Segmented Permanent Magnet Synchronous Machines for Wind Energy
Conversion System
Wenying Jiang
'
Patel B. Redd
wjiang4@wisc.edu
,
/
T.M. Jahns
reddy@ge.com
T.A. Lipo
jahns@engr.wisc.edu
3
Ramasamy Anbarasu
4
Henrik Lykke Sprensen
Mohamed Osama
anbarasu@ge.com
h.l.sorensen@hotmail.com
osama@ge.com
2
University of Wisconsin - Madison
Madison, WI
4
GE Global Research Center
USA
Niskayuna, NY
5
Consultant
Munich, GERMANY
Abstract-Direct-drive generators are appealing candidates for
some wind energy conversion systems (WECS) since they
provide
a
means
of
eliminating
the
gearbox
from
the
drivetrain. However, a fundamental problem associated with
these machines is their large size that makes them difficult to
manufacture, transport, and assemble. This paper introduces
concept
of
segmented
permanent
magnet
(PM)
synchronous machines with both single and dual stator/rotor
layers that feature a modular structure which makes them
appealing candidates for use in direct-drive wind generators.
To form a multi-phase machine, a spatial phase-shifting iron
piece is inserted between adjacent segments to maintain the
appropriate
spatial
positioning
between
phases.
The
segmentation strategy for this type of machine is discussed,
considering the trade-offs between average torque production
and torque ripple. A nine-phase segmented
PM
synchronous
machine configuration is proposed for reducing torque ripple
and improving fault-tolerance capabilities. The performance
characteristics of this segmented machine configuration are
evaluated using finite element (FE) analysis.
I.
INTRODUCTION
The wind turbine drivetrain including the generator plays a
major role in determining the overall performance
capabilities of a wind energy conversion system (WE CS).
Because of the low rotating speed of the wind turbine, a step­
up gearbox is generally applied to increase the generator
shaft speed and reduce its mass and volume. Unfortunately,
the adoption of a gearbox contributes vibration and noise,
increases losses, and requires lubrication as well as regular
maintenance.
Therefore, direct-drive generators that
eliminate the gearbox from the drivetrain have been
receiving serious attention as candidates for WE CS
applications
[ 1-4].
These generators are generally
characterized by large dimensions and mass, making them
difficult to manufacture, transport, and assemble. As a result,
segmented construction of direct-drive generators is of high
interest [5].
Among various types of generators evaluated for use in
low-speed applications, permanent magnet ( PM) machines
978-1-4799-5138-3/14/$31.00 ©2014 IEEE
5
'
lipo@engr.wisc.edu
6
Martin V.R. Skov Jensen
mvsj@vestas.com
3
GE Energy Power Conversion GmbH
Berlin, GERMANY
USA
GE Global Research Center
Aarhus, DENMARK
the
'
6
Vestas Wind Systems A/S
Aarhus, DENMARK
are attractive candidates that offer several advantages
including high efficiency and torque density. Although the
price of rare-earth PM materials has been vulnerable to wide
swings, PM synchronous generators continue to draw
attention for use in large direct-drive wind turbines [6-8].
More
specifically,
surface-mounted
PM
machine
configurations have been adopted in many investigations due
to their high torque density and compatibility with large
airgaps [ 1,4],
Optimization techniques are desired for this type of
generator in order to improve their torque density and reduce
the material cost. There are many different optimization
algorithms used for the purpose of machine design
optimization. Differential evolution (DE), particle swarm
optimization ( PS O), and genetic algorithm (G A) are the three
optlllllzation algorithms discussed most widely in
publications [9- 12]. DE, PS O, and G A all fall into the class
of population-based, stochastic function minimizers. As
such, they are all well-suited for machine design
optimization, which is a nonlinear and constrained problem
involving both continuous and discrete variables.
Comparisons between DE and many other optimization
algorithms have been reported in a recent study [ 13]. The
results show that DE may not always be the fastest method,
but it is usually the one that produces the best results, and
there are frequent cases in which it is the fastest algorithm as
well. Since DE is a population-based algorithm, it is suitable
for adoption in a distributed parallel computing environment.
This paper introduces the concept of segmented permanent
magnet ( PM) synchronous machines with three different
stator-rotor arrangements: single-rotorlsingle-stator (SRSS),
double-rotorlsingle-stator (DRSS), and single-rotor/double­
stator (SRDS). Their modular structure makes them very
suitable for application to direct-drive wind generators. To
form a multi-phase machine, a phase-shift iron piece is
inserted between adjacent segments to maintain the
appropriate spatial pOSItioning between phases. The
segmentation strategy for this type of machine is discussed,
! '\
\\\
PhaS9C/
/
./
//
Phase a
,
\
"\\
Fig. 1: Segmented PM machine concept shown for three-phase machine
Fig. 3: Developed view of one segment of DRSS PM machine
t
Fig. 2: Developed view of one segment of SRSS PM machine
considering the trade-offs between torque production and
torque ripple. A nine-phase segmented PM synchronous
machine configuration is presented with the objectives of
reducing torque ripple and improving the machine's fault
tolerance capabilities. An optimal design has been developed
with the objective of achieving high torque density and low
magnet consumption, and its performance is evaluated using
finite element (FE) analysis.
II.
SEGMENTED PM SYNCHRONOUS MACHINE CONCEPT
The basic concept of a segmented PM synchronous
machine is illustrated in Fig. 1, showing that the machine is
evenly divided into 6 arc segments (or another multiple of
three for three-phase machines). Each segment in a single­
rotor single-stator ( SRSS) arrangement (Fig. 2) is occupied
by a single phase with uniformly-spaced teeth and slots. Its
slot pitch equals the pole pitch, yielding the highest possible
winding factor of unity that is a key to achieving high
machine torque density. To form a three-phase machine, iron
pieces with a span equivalent to 60 or 120 elec. degree
spatial phase shift are added between adjacent phase
segments in the stator [ 14].
On the rotor side, permanent magnets are mounted on the
surface of the iron core. This rotor configuration has
demonstrated appealing performance advantages including
high efficiency, high torque density, low rotor losses, and
compatibility with high airgap lengths [ 15]. For the stator,
single-layer concentrated windings are wound around every
second tooth providing a cost-effective design that eases
stator fabrication, shortens end windings, increases the slot
fill factor, and enhances the machine's fault tolerance
Fig. 4: Developed view of one segment of SRDS PM machine
characteristics [ 16]. All of these features associated with the
segmented PM synchronous machine make it a very suitable
candidate for the direct-drive wind generator.
The segmented PM machine concept can be extended to
machines with dual-stator or dual-rotor layers that have two
airgaps that must be structurally maintained. The dual-layer
segmented PM machine can be classified into two major
types: the double-rotor/single-stator (DRSS ) machine, and
the single-rotor/double-stator ( SRDS) machine. The basic
stator-rotor configurations for one segment of these two
machine types are presented in Figs. 3 and 4. It should be
noted that the structure of each individual stator/rotor layer
in both of these dual-layer machines is identical to that of the
SRSS machine in Fig. 2.
For the DRSS machine (Fig. 3), the magnets are arranged
so that the magnetic fluxes in the central stator yoke shared
by both layers will cancel during normal operation, assuming
that the dimensions and winding details in both layers are
identical. This canceling effect makes the shared stator yoke
electromagnetically inactive. As a result, the stator yoke
thickness can be minimized or, in the limit, reduced to zero
to minimize the machine active mass without interfering
with its electromagnetic performance. However, the
structural integrity of the stator must still be maintained. This
same flux nulling feature can be designed into the central
rotor yoke of the SRDS machine (Fig. 4), making it possible
to reduce the yoke thickness and associated rotor mass.
TABLE l. SPECIFICATIONS FOR DIRECT-DRIVE WIND GENERATORS
Parameter/Metric
Value
Power Rating
6 MW
Corner Speed
11.3 r/min
Maximum Speed
15 r/min
Line-to-Line Voltage
690 Vrms
Airgap (Inner) Diameter
10 m
Stator Length
<1 m
Airgap Thickness
10 mm
Current Density
4 Almm2
Copper Fill Factor
50%
Copper Resistivity
25 nQ-m @ 150 °C
Steel Laminations
MI9,0.35 mm
NdFeB Magnet Remanent Aux Density
1.1 T @ 150 °C
Sintered NdFeB Magnet Resistivity
1.4 f.\Q-m
Maximum Excitation Frequency
Demagnetization Threshold
Copper Density
Steel Density
Magnet Density
>
150 Hz
3x rated current
8940 kg/m3
7850 kg/m3
7450 kg/m3
Lamination Steel Price
US$I/kg
Copper Price
US$5/kg
NdFeB Magnet Price
US$55/kg
Both of the airgaps in the two dual-layer machine
configurations can develop the same shear force,
contributing nearly the same amount of torque in both layers
that differ only by the ratio of the two airgap radii.
Therefore, the stack length of a dual-layer machine is
approximately half that of a SRSS machine to satisfy an
equivalent torque requirement, assuming that the dimensions
are essentially the same in both stator-rotor layers and the
sustainable current densities in the winding slots are the
same for both the single- and dual-layer machines. The
shortened stack length is beneficial to ease the mechanical
stress associated with transporting and assembling this type
of large machines.
The presence of two airgaps in the dual-layer machines
offers both challenges and opportunities. Mechanically
maintaining both airgaps requires special attention in the
structural design, particularly if a cantilevered rotor design is
adopted with bearings only on one axial end of the machine.
However, the radial forces in the two airgaps cancel,
simplifying the mechanical design task to some degree.
Cogging torque can also be reduced by properly aligning the
two stator-rotor layers [ 17, 18].
III.
Fig. 5: One segment (pole-pair) cross-section of a single-phase SRSS
PM machine
50
100
150
200
250
Electrical Angle [degree]
300
350
Fig. 6: FE-predicted torque waveform of the single-phase SRSS
PM machine @ 6 MW,11.3 r/min
UO�te.C"l .. 1
O"Cl'""Spatlo'l
Ph.. Shift
Fig. 7: Three-segment cross-section of a three-phase SRSS PM machine
Ox10
6
-1
SEGMENTATION STRATEGY
A preliminary design for a single-phase SRSS segmented
PM synchronous machine with 272 pole pairs has been
developed according to the specifications listed in Table I for
a direct-drive wind generator application. One pole-pair
cross-section is shown in Fig. 5. For a single-phase machine,
there is no need for any extra iron pieces in the stator for
spatial phase shifting, resulting in an equal number of stator
slots and rotor poles. The unity winding factor feature noted
-
60�--�5�0--�1�00��1�5�0--�2�0�0--�2�5�0�-3�0�0��35:C:0
Electrical Angle [degree]
Fig. 8: FE-predicted torque waveform of the 3-phase SRSS PM machine
@ 6 MW,11.3 r/min
40 E/�ctrical D�gru
Phas�Shjft
D
c
F
(7 pole-pairs per phase-belt' 9
•
3) +(3 interstitial pole
" 192 pole-pairs
Fig. 9: 9-phase segmented SRSS
PM
synchr. machine with 192 pole-pairs
earlier contributes to maximizing the torque production
capability. However, this basic topology suffers from severe
torque pulsations as evident in the torque waveform
generated by FE analysis (Fig. 6).
Next, a preliminary design for a three-phase version of
the SRSS machine has been developed by inserting an iron
piece representing a 120 elec. degree spatial phase shift
between every adjacent slot/pole-pair (Fig. 7).
The
dimensions of the rotor and stator slots are the same as for
the single-phase machine. This is an extreme design for
three-phase segmented PM machines since only 75% of the
stator circumference (i.e., the slots) is actively involved in
the electromechanical energy conversion process due to the
large number of passive phase-shifting segments. As a
result, the stack length of this three-phase machine is 42.5%
longer than the single-phase machine in order to meet the
torque production requirement.
On the other hand, the
spatial phase shifting has significantly reduced the torque
pulsations to 9.6% (peak-to-peak) of the rated torque as
shown in Fig. 8.
There are many different ways to segment this type of
machine, especially for the direct-drive wind turbine
application where a high pole number is required to meet the
high-torque, low-speed specifications. Adding spatial phase­
shifting iron pieces into the stator generally leads to a
reduction in average torque production, but an improvement
in torque ripple. Proper selection of the number of phases
and segments can reduce the torque ripple of the segmented
PM machine to fall within an acceptable range while
minimizing the loss in average torque production capability.
This segmentation strategy also applies to the dual-layer
segmented PM machines (DRSS and SRDS), for which each
layer exhibits electromagnetic characteristics that are almost
identical to those of the SRSS machine.
IV. NINE- PHASE SEGMENTED PM SYNCHRONOUS MACHINE
Multi-phase generators can offer a variety of advantages
including low torque ripple, high fault tolerance, and reduced
current and voltage stress on the switching devices.
Applications of this approach have typically been focused on
machines with phase numbers that are multiples of three
because of the prevalent use of three-phase converters. For
this work, a nine-phase machine has been identified to be an
appealing candidate for a segmented PM machine intended
for a direct-drive wind application.
Taking practical issues associated with manufacturing and
transporting this large machine into account, a nine-phase
segmented PM synchronous machine with 192 pole-pairs has
been investigated with the objectives of reducing the torque
ripple and improving the machine's fault tolerance
capabilities. The resulting machine configuration is
summarized in Fig. 9 that shows one of the machine's phase
segments. A dovetail tooth structure has been adopted to
mechanically secure the 384 magnet pole pieces in place.
The stator is sliced into 27 segments, and each segment is
approx. 1 m in arc circumference. In each segment, there are
7 active pole pairs ( 14 slots), together with a phase-shifting
iron piece that provides a 40 elec. degree phase shift between
adjacent stator segments. The phase shift is 180 elec. degrees
between adjacent slots within each segment. Hence coil sides
"+" and "-" form a single coil, corresponding to a single­
layer winding. All seven coils together form a single phase
belt, as shown in Fig. 9. The slots are assumed to be fully
open in this preliminary design.
The total number of active pole-pairs on the stator side is
7*27
189, while all of the interstitial phase shift iron pieces
add up to 3 electromagnetically inactive pole-pairs (40
deg.*27/360 deg.
3). Summing both the active and
inactive parts together, there is the same number of pole­
pairs on the stator and rotor, as required.
=
=
V. ApPLICATION OF OPTIMIZATION TECHNIQUES
A. Optimization Algorithm: Differential Evolution (DE)
The SRSS segmented PM synchronous machine with 192
pole-pairs has been designed using optimization techniques
[ 19] to achieve high torque density and low material cost
(i.e., low magnet mass). The implementation of FE analysis
is based on the machine design optimization flow diagram
presented in Fig. 10. The DE optimization algorithm written
in M A TL A B provides the outer shell of the optimization
program that governs the optimization process. It is a
generation-based algorithm, so it provides the opportunity
for parallel analysis of all designs within each generation.
Through the stages of initialization, mutation, crossover, and
selection, DE is explores the entire design space and locates
the global optimum with high confidence [ 14]. Each of these
stages is described brie fly as follows:
1.
Initialization
( 1)
where x represents the vector of adjustable machine design
variables. The subscript 0 represents the initial generation
(i.e., 9 = 0), j and i represent the /h parameter of the ith
Fig. 11: Segmented PM machine design variables
TABLE II. SEGMENTED PM MACHINE VARIABLE DEFINITIONS AND
RANGES
Variable Parameters
Tooth Width to Rotor Pole Pitch Ratio
Stator Yoke Thickness to Tooth Width Ratio
Fig. 10: Flow chart of machine design optimization algorithm in
high-throughput computing environment [19].
2.
Mutation
(2)
·
In the 9 th generatlOn,
Xro,g, Xn,g and Xr2,g are three
randomly selected vectors of machine design variables. The
mutant vector Vi,g is created by adding a scaled vector
difference to the new vector. The scale factor, F E (0,1 +),
is an adjustable user-defined scalar variable that controls the
rate at which the population evolves.
3.
Crossover
U'r,g
=
u..
j,r,g
=
f Vj,i,g if (randj(O,l) � Cr)
.
t
x· ,r,
otherwise.
j g
(3)
The trial vector Ui,g is assembled from parameter values
that have been copied from two different source vectors: the
mutant vector Vi,g and the current vector Xi,g' The crossover
probability, Cr E [0,1], is a user-defined value that controls
the fraction of parameter values that are selected from the
mutant vector.
4.
Selection
X.r,g
+l
=
f Ui,g if f(ui,g) � [ (Xi,g )
t
Xi,g otherwise.
(4)
A user-defined objective function f is used to evaluate
performance metrics of all candidate designs. DE uses
objective function results to formulate choices that determine
[0.1,1]
Magnet Span to Rotor Pole Pitch Ratio
[0.7,0.9]
Rotor Yoke Thickness to Rotor Pole Pitch Ratio
[0.1,0.5]
Magnet Thickness to Airgap Thickness Ratio
vector in the initial generation of variable vectors, rand is a
random scalar number between ° and 1, and bL, bu are
initialization lower- and upper-bound vectors, respectively.
Range
[0.3,0.5]
[1.1,3]
the next generation of designs. The design performance
improves with each generation. Once the pre-specified
termination criterion is satisfied, the iterative optimization
process ends.
B. FE Analysis-based Machine Design Optimization
The optimization is implemented based on a single-phase
SRSS segmented PM machine configured with 384 rotor
poles, which can be easily extended to the nine-phase
machine by inserting spatial phase-shifting iron pieces as
discussed in Section IV. Each FE model for one pole-pair of
a candidate SRSS segmented PM machine can be defined by
a set of parameters, both fixed and varied. The fixed
parameters are defined by the machine specifications listed
in Table I. The five variable parameters are identified in Fig.
1 1, including the stator tooth width, stator yoke thickness,
magnet span ratio, rotor yoke thickness, and magnet
thickness. The ranges for these variables, shown in Table II,
are defined as ratios rather than absolute values in order to
help ensure that each candidate design meets all of the
geometric constraints. The range boundary values have been
chosen to ensure that the optimum values fall within the
allowable design space.
Next, all of the parameters in the parameter set are fed into
the template Visual Basic (V B) script for FE analysis that
contains information about the machine configuration,
material, and excitation to create a specific script for each
candidate design. The performance of each candidate design
is evaluated when the current angle is aligned with the q-axis
in order to achieve maximum torque per ampere (M T P A).
Ca!>el
Case2
Torque
5 .0725 E "' 06
5 .0720 E.,.06
) .071S E+06
f
�
Case 3
f;1
F
KXX)I/,\.
KXX><l
�,
:' .068 3 E.,.06
x_x •• _
•• j( •••
)0<; )0<; � , ,
o
Case2
Case3
Case4
CaseS
Stack Length [m]
0.763
0.900
0.866
0.940
0.930
Magnet Height [mm]
24.38
14.03
14.77
11.08
11.26
Magnet Span Ratio
0.898
0.891
0.880
0.897
0.713
Copper Mass [kg x103]
5.58
6.58
6.35
6.91
7.01
Magnet Mass [kg x103]
3.78
2.55
2.55
2.11
1.68
Total Mass [kg x103]
MatI. Cost [$USx106]
20.96
21.84
22.07
23.75
33.63
0.252
0.190
0.189
0.170
0.156
Effie. @ 6 MW [ %]
92.86
93.09
93.11
93.23
93.37
The candidate machines were designed for rated operating
conditions, i.e., n = 11.3 rlmin, P = 6 MW, and T = 5.07
M Nm, where n, P, and T represent the rotor speed, output
mechanical power, and torque, respectively. The objective
function has been defined as
TD
TPD
(5)
OF
a*
+b*
TDBase
TPDBase
=
--
---
where TD represents torque density [ Nm/kg], TPD
corresponds to torque per dollar [ Nm/$ US], O:s; a:s; 1,
b =1
a,
TDBase = 250 Nmlkg, and TPDBase = 30
Nrn/$. The values of TDBase and TPDBaSeare determined
based on the results of preliminary optimization runs with
objective functions focused on maximum torque density and
minimum material cost, respectively. In order to understand
the trade-offs between improving torque density and
reducing material cost, five combinations of a, b values are
used in the objective function as follows.
-
�
Case 1:
a
= 1,
�
Case 2:
a
= 0.7,
b = 0.3;
�
Case 3:
a
= 0.5,
b = 0.5;
�
Case 4:
a
= 0.3,
b = 0.7;
�
Case 5:
a
= 0,
001
0 . 02
003
Time Imsj
OPTIMIZED SEGMENTED SRSS PM MACHlNE DETAILS
CaseI
IJrtJ .
5 . 069SE"' 06
5 . 0690E"-06
Fig. 12: One pole-pair cross-sections of the five optimized segmented SRSS
PM machine designs
TABLE IlL
10' d
_e.
5 .070:;E"'06
o 5 .0700E.,.06
CueS
Case 4
5 .0710E ... 06
b = 0; (Maximum torque density)
b = 1. (Minimum cost)
Fig. 12: FE-predicted torque waveform (with expanded scale) for the opti­
mized Case 3 9-phase segmented SRSS PM synchronous machine @ 6 MW
Based on previous experience, the control parameters for
the DE optimizer were chosen to be: convergence tolerance
Tal = 10-6; number of designs in each generation NP =
85; crossover probability Cr = 0.8; and scale factor F =
0.8.
C.
Optimized Designs
The five optimizations were then run, and they converged
to designs optimized for maximum torque density ( Case 1),
minimum cost ( Case 5), and a combination of high torque
density and low cost ( Case 2, 3, and 4). The resulting single
pole-pair cross-sections of these SRSS machine designs are
shown in Fig. 12, and key dimensions and metrics for the 5
optimized machine designs are summarized in Table III.
It can be observed from Fig. 12 and Table III that the Case
1 design, optimized for maximum torque density, has the
thickest magnets, shortest stack length, highest magnet mass,
and highest material cost. The optimized minimum-cost
design ( Case 5) has the lowest magnet mass but highest total
mass, and lowest material cost. The Case 2 design with its
objective function emphasizing high torque density performs
more like the Case 1 design, while the Case 4 design,
optimized with priority on reducing cost, exhibits similar
characteristics as the Case 5 design. The performance of the
Case 3 design, optimized for both high torque density and
low cost, is situated in the middle among the five optimized
designs.
For the efficiency evaluation, only the dc resistance is
considered when calculating the copper loss, consistent with
the low excitation frequency «50 Hz). The core loss is
estimated using JM AG, a commercial FE analysis package.
The magnet loss is not included in the efficiency calculation
since it is negligible for this low-speed application with
adequate magnet segmentation. The rated power operating
point efficiencies for all of the five optimized designs are in
the vicinity of 93%.
1.5
(],I
tlO
ttl
......
g
.......
......
c
�
....
::J
U
"0
(],I
.!::!
ttl
E
....
0
Z
:B [TI
--Normalized Current
1.2
-Normalized Voltage
1.0
2.0
1.8
1. 6
0.5
Applied along
eg ative d-A)(is
U
1.0
0.8
-0.5
0.15
0. 4
-1.0
0.2
0.0
-1.5
Fig. 13: FE-calculated nonnalized phase current and voltage waveforms of
the nine-phase segmented PM machine under rated operation
Normalized Current
�06
A. Torque Ripple
E
�
<'30.4
0.2
10
20
Harmonic
30
40
Fig. l4: Harmonic spectrum of the FE-calculated nonnalized phase current
during rated power operation at 6 kW with sinusoidal current excitation.
Normalized Voltage
0.9 n=---�---�-----'
0.8
0.7
0.6
�
'" 0.5
0)
'"
'604
0.3
0.2
0.1
Fig. 16: FE-calculated flux density contour plot inside one rotor pole magnet
for the nine-phase segmented PM machine with 3 x rated current applied
along the negative d-axis
in Fig. 9. This model has been used by the FE analysis
software to evaluate the performance characteristics of the
nine-phase segmented SRSS PM synchronous machine
under the assumption of balanced nine-phase sinusoidal
current excitation.
0.8
_I.
0� ��--��--uu--�uu----� �--uu�
10
40
30
2O
0
Harmonic
Fig. 15: Harmonic spectrum of the FE-calculated normalized phase voltage
during rated power operation at 6 kW with sinusoidal current excitation.
VI.
Dens ity Vectors
1.2
0.0
>
flux
with 3xR a te d C u r rent
PERFORMANCE CHARACTERISTICS OF THE NINE-PHASE
SEGMENTED PM SYNCHRONOUS MACHINE
A FE machine model that includes all nine phase windings
and spatial phase-shifting between the adjacent phase belts
has been assembled based on the dimensions of the
optimized Case 3 design, leading to the configuration shown
The torque waveform of this machine has been analyzed
under rated operating conditions, as shown in Fig. 12. The
peak-to peak torque ripple is less than 0.07% of the rated
torque. The negligible torque ripple is one of the appealing
features of this nine-phase segmented PM synchronous
machine configuration.
B. Harmonic Spectra and Power Factor
Figure 13 shows the normalized phase current and phase
voltage waveforms of the nine-phase segmented PM
machine under rated operation. The voltage waveform was
obtained by placing voltage probes at winding terminals in
the FE model. The harmonic spectrums of the two
waveforms have been analyzed using the Fast Fourier
Transform (FF T) as shown in Fig. 14 and 15.
Since the current waveforms are assumed to be ideally
sinusoidal, only the fundamental component is evident in the
current waveform harmonic spectrum (Fig. 14). In contrast,
the presence of the third and fifth harmonics in the phase
voltage waveform (Fig. 15) has a degrading impact on the
machine's terminal power factor. The fundamental current
vector lags the fundamental voltage vector by 47.3°, leading
to a low displacement power factor of 0.67. The impact of
end winding leakage inductance is not considered in this
power factor calculation. Identifying techniques for
improving the machine's power factor is an important topic
for future investigation.
C.
Demagnetization
The flux densities in the magnets of the nine-phase
segmented PM machine have been evaluated by applying
three times the rated current applied along the negative d-
axis in order to examine the machine's demagnetization
characteristics. The resulting flux density color contour plot
inside one of the rotor pole magnets is presented in Fig. 16.
The lowest magnet flux density inside the bulk magnet is 0.4
T, indicating there is no sign of demagnetization under this
operating condition.
It can also be observed in Fig. 16 that the magnet regions
closest to airgap experience higher demagnetization effects
compared to bulk magnet material that is far away from the
airgap. The demagnetization risk for this machine
configuration is relatively low, consistent with the large
airgap that provides a level of protection.
VII.
CONCLUSIONS
This paper introduces the concept of segmented permanent
magnet (PM) machines with both a single-statorlsingle-rotor
configuration and dual stator or dual rotor layers,
highlighting their modular structure that makes them very
suitable for application in the direct-drive wind generators.
Multiple-phase segmented machines can be constructed by
inserting spatial phase-shifting iron pieces among the stator
segments. The proper selection of the phase number and
segment number helps to suppress the machine's torque
ripple while minimizing the loss in average torque
production.
A nine-phase segmented PM synchronous machine
configuration has been proposed with the objectives of
reducing the torque ripple and improving the machine fault
tolerance capabilities. Five segmented PM machine designs
have been optimized for maximum torque density, minimum
material cost (magnet mass), and combinations of both
objectives, using an iterative FE-based machine design
optimization algorithm based on differential evolution.
Finite element analysis results demonstrate that this
machine configuration is capable of developing high average
torque with low torque ripple, while exhibiting low
vulnerability to demagnetization. These promising results
confirm that segmented PM machines offer attractive
features for direct-drive wind turbine generators and other
applications requiring high torque at low speeds.
ACKNOWLEDGMENTS
The authors are grateful to Vestas Wind Systems for
providing financial support, and also to JS OL Corp. and
Infolytica Corp. for making their finite element analysis
packages available for this investigation.
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